宏观物理学的哲学和数学反思

第一卷

Philosophical and mathematical reflection on macroscopic physics

Vol. Ⅰ

湍流及理论流体力学的理性重构

Turbulence and reconstruction of theoretical fluid dynamics

杨本洛

(上海交通大学)

（2001年9月初稿）

内容简介

       本书是《宏观力学基础分析 —— 宏观物理学的哲学和数学反思》的第一卷。与其说本书是一本流体力学的教科书或者一般意义上的专著，不如将其称之为一本论述整个理论流体力学基础的论文集。仅仅为了便于流体力学研究者能够独立考察和研究他们感兴趣的不同论题，本书各章基本上自成体系。这些不同的论题分别涉及流体物质元的形式表述、流体力学的一般动力学方程、流场的动力学边界条件、流体力学不同形式动力学方程的不同物质基础与它们之间的逻辑关联、以及对“表观应力”、“热力学压力”等基本概念加以重新诠释等。在物理内涵和形式表述两个方面，几乎所有的相关结论都与经典理论存在一定的差异。本书适合于应用数学、理论物理、流体力学以及科学哲学等相关专业的科学研究者，工程技术人员，教师和研究生阅读。

序

       许多年来，在基础科学许多互为相关的研究领域中，我校杨本洛教授发表了一系列的独立研究结果。

       在杨本洛教授的基础研究中，反复提出自然科学研究中的“物质第一性”原则和“逻辑自洽性”原则的问题。从形式逻辑考虑，当人们以自存的物质世界作为自然科学的特定研究对象时，做出这样一种形式上的明确认定或许是有意义的，尽管这样一种认识对于某些经典理论可能构成某种冲击。

       但是，无论这些研究结果是否完备、恰当，乃至最终证明是否正确，努力使用严格的科学语言，进行科学意义上的严肃探讨，对于自然科学研究中许多基元概念提出独立看法的这一事实本身是重要的。

       可以相信，只有切实支持原创性的基础研究，允许和鼓励在严肃科学意义上的不同学说观点的发表和争论，才可能使我国的独立基础科学研究真正容入世界科学发展的进程，并且，能够为实现中华民族的伟大复兴发挥更大的作用。

上海交通大学校长

谢绳武

2002年末

《宏观力学基础分析》

总 目

坚持自然科学研究中的物质第一性原则和逻辑自洽性原则

       －《宏观力学基础分析－宏观物理学哲学和数学反思》总序

卷Ⅰ：湍流和理论流体力学理性重构

卷Ⅱ：宏观物质粒子本质和热力学理性重建

卷Ⅲ：经典宏观力学若干基本概念的澄清

Total contents

for

Analysis on the fundamental of macroscopic mechanics

—     Philosophical and mathematical reflection on macroscopic physics

 

Persistence of material primary and logic consistence principles in natural science

- Overall preface to Analysis on the fundamental of macroscopic mechanics – Philosophical and mathematical reflection macroscopic physics

Volume 1: Turbulence and reconstruction of theoretical fluid dynamics

Volume 2: Particle essential of macroscopic material and rational rebuilding of thermodynamics

Volume 3: Clarification on elementary concepts in classical mechanical mechanics

坚持自然科学研究中的物质第一性原则和逻辑自洽性原则

《宏观力学基础分析－宏观物理学哲学和数学反思》总序

       湍流被现代科学世界称之为世纪之交，大自然对人类一次最严峻的考验。虽然对于任何一个严肃的理论流体力学研究者，或者致力于整个理论物理基础研究的工作者，几乎难以回避这样一个自然科学中的重大课题。但是，对于笔者而言，能够较为深入的考虑湍流，或许应该完全归于一种偶然。事实上，作为一个一般工程技术领域中的教学研究人员，笔者仅仅源于工作的某些需要以及对于探求未知的一种真诚，不自觉地步入了这个充满挑战的自然科学的纯粹基础研究领域。

       近若干年，笔者出版了几本和“热力学”、“流体力学”、“相对论”相关，以及涉及“Newton经典力学”、“电磁场理论”等整个“自然科学哲学和数学基础”的专著，期望本着一切科学陈述必需共同遵守的“逻辑自洽化”原则，对于宏观力学乃至与整个理论物理基础相关的一系列前提性问题进行了分析。

       毋庸置疑，许多观点、提法和导得的结果与得到目前科学主流社会认同或者极力维护的

经典认识存在相当大差异。但是，理性是批判不倒的。如果经典认识的确存在无法回避的矛盾和错误，那么，通过严肃的科学语言，针对经典理论所进行的批判只能说明：人们长时间形成的经典认识本身真实地存在需要重新认识之处。当然，认识的重新认识同样难免出现新的问题和错误。正因为此，并且，像人们熟知的那样，在到底何为“惯性系”、何为“湍流”、如何理解“物质世界非对称性以及物理世界对称性”矛盾，以及如何为“量子力学”建立一个可信的哲学基础等的许多方面，都存在关系到整个自然科学存在基础的前提性问题，那么，人们没有理由拒绝批判。并且，只能通过认识差异的揭示，借助于严格的数学语言，努力以“无矛盾”原则为基本准绳展开科学意义上的严肃批判，才可能使得人们在一个新的认识层次上重新取得共识。可以坚信，只有打破经典认识的一统天下，人们所说的许多世纪性难题才可能真正得到解决。

       今年春夏之交，得以与中国自然科学基金委员会中一些热心于人类科学事业以及中国自然科学如何真正步入世界科学之林的同志进行了初浅的探讨。他们提议召开一个国际研讨会，以能够首先针对我在流体力学领域的研究结果与国内外的学者进行交流。为此，需要我首先将自己所提的一些基本观点加以整理。当然，在我的基础科学研究长时间处于一种被人为封闭状态之际，如果能够获得这样一次极为难得的机会，是极其难得和不易的，我自然予以十分的珍惜。

       现在看来，使我格外感到珍惜，同时又是意料之中与意料之外的是：当我经历了在“宏观物理学”方面的许多思考，将主要精力集中在自然科学体系中其它方面，在诸如“Newton经典力学”、“相对论”以及“电磁场理论”等研究领域中获得一系列有别于经典认识的结论，重新较为系统地考虑宏观力学中一些基本问题的时候，我发现这些年来的许多分析和陈述其实仍然远不深刻和准确。或者说，在一些基本思维理念上面，对于经典理论体系整体存在问题本质内涵的认识和批判远远不够，以致若干相应陈述并不准确，本质上存在对于“重新认识中的认识”进行进一步重新认识和批判之处。因此，并不仅仅需要对演绎推理过程中个别地方出现的差误应该予以修正，更为重要的是需要深化曾经进行的批判，真正摆脱经典认识中关于“物质描述”一种根深蒂固的思维束缚。

       与其对应，在如何表现宏观物质复杂运动方面，笔者经历了从严厉批判经验湍流模型所显示的不确定性，到重新确认以大数粒子集合为本质内涵的宏观物质在其运动过程中必然蕴含的“非确定性”这样一个重新认识和自我批判的过程。并且可以逻辑地确认，经典物理学定律对表现宏观物质的一般运动“恒”不具“形式完备性”。在这种特定意义上，任何形式表述的变分原理，仅仅为人们合理地描述宏观物质复杂运动提供了一种可信的基本原则。但是，离开对于某种流动结构的经验确认，任何仅仅被赋予纯粹形式意义的变分原理，并不能成为某种具有实际可操作性的独立计算模式。可以相信，如果说任何认识的真正深化必然真实地需要一个反复深化认识的艰苦劳动过程，那么，目前针对宏观物理学所作不同形式的“理性重构”或者“理性重建”，仍然是这种认识深化过程的继续，必然存在许多需要进一步深刻化的内容

       也正因为此，在自然科学研究中，需要重新确信本质上以“逻辑自洽性”为内核的“科学理性”。特别是，当一些诚实的科学家公然将“理论物理中的数学严谨性”称之为“自欺欺人”，并且，以此作为理由，自觉或者不自觉维护目前自然科学体系中一种普遍存在的“过分形而上学”的基本秩序，乃至由此而产生的某种所谓的“科学宗教”情结的时候，重新真诚呼唤以“无矛盾”原则为最根本判据的“科学批判”，对于当今的整个科学世界显得更为迫切和重要。

       自然科学仅仅是人类认识体系中一个极其有限的部分。作为一种基本界定，自然科学所描述的只是大自然中形形色色的不同特定物质对象。因此，即使抛弃“有神论与无神论”或者“唯心主义与唯物主义”的争论，而仅仅从形式逻辑考虑，那个被人们描述的特定物质对象对于整个形式系统必然具有前提性的根本意义。这样，从基本的哲学层面考虑，在从“Newton经典力学”直到“现代量子力学”的整个自然科学体系中，那个普遍真实存在以对于某些“特定方程”或者“特定关系”的认同作为构造某一些形式系统的“基本前提”或者“公理化基础”的习惯认识，需要做出彻底的转变，代之以针对特定物质对象所作“理想化认定”作为构造一个公理化体系的唯一前提。此时，描述整个物质世界的语言必须是“同一”和“无歧义”的，人们无须也不可以为不同的物质世界，例如所谓的“宏观物质”和“微观物质”构造彼此相悖的不同原则。不同物质对象所表现的不同形式特征，根本决定于对于不同物质对象所作基本合理的理想化认定。

       当现代科学世界几乎无法遏制人们对于“相对论”进行批判和重新认识的时候，一个重要的问题在于：不仅是“相对论”，而且是自Newton经典力学开始的整个自然科学体系都忽略了如何对被描述对象首先做出具有明确意义的形式认定这样一个重要的基本原则。当然，正是因为这样一个前提性的问题没有真正得到解决，一个仅仅条件存在并且有限真实的形式表述往往被误认为一种普遍的真理，无论这样一种错觉是自觉还是不自觉的。

       事实上，当真诚的Einstein以对于整个物质世界必然存在某种特定联系的信念作为他的全部思维基础，并且，将他所说的一对“无须也不允许”加以解释的“矛盾着的真实 —— ‘光速不变原理’和‘相对性原理’”界定为整个“相对论”得以存在的全部前提时，正如人们已经看到那样，他以及他的追随者也同样“不能也无须”对这个理论体系做出任何解释。正因为此，这种存在于当今科学世界中一种十分奇特的宗教式的虔诚，只能成为被当今自然科学的主流社会称之为一种“宗教情结”。其实，究其本质，“时空观”革命的目的无非在于通过改变“形式语言”自身的内涵，以能够对无尽大自然中的许多真实存在做出某种“同一化”的解释。当然，一个以真实存在的“矛盾”为基本前提的理论体系，如果不存在形式推理过程中的错误或者紊乱，这个理论体系则始终是一个“矛盾”体系。仍然从形式逻辑考虑，相对论中被视为“统一度量基准”的一对不变的“原时和钢尺(Proper time and rigid ruler)”，已经将相对论重新引入到Newton的时空观之中。

       事实上，不仅仅像笔者在《自然哲学基础分析 —— 相对论的哲学和数学反思》一书中已经阐明的那样：对于经典的“Newton运动定理”，如果对该定理形式定义的“力”所涉及到的“全部物质存在 —— 受力体和施力体”同时做出了具有形式意义的界定，那么，以“循环定义”为本质特征的“惯性系”，以及由于“无穷多惯性系”的存在而引起物理学中所有与运动学状况有关的物理学量的“非确定性”问题将不复存在；同时，一旦意识到“电磁场”与作为“电磁场的源”而存在的“电荷和电流分布”的相互依赖关联，那么，地磁场中的电磁波独立于地球的运动将成为一个十分自然的事实，也恰恰于此，Michelson-Morley实验所测得“以太相对于地球的速度恒为零”将成为一个同样自然的结果。可以相信，物质世界的可解释性，绝非人类可能为某一种真实存在提供它得以存在的某种理由。物质世界的可解释性，本质上仅仅在于一切抽象同一的物质对象必然共同存在的抽象同一性，或者自然科学陈述的无矛盾性。因此，人们同样可以确信，当、且仅仅当“量子力学”能够对所研究的物质对象做出一种基本符合物理真实的形式界定，并且，由此提供一个同样具有确定意义的“有限论域”的时候，那么，量子力学中许多实质性的陈述同样是自然和合理的，必然吻合于整个物理学对于物质世界的理性陈述，而无须为这个所谓的“微观理论体系”单独构造属于自己的语言或者基本原则。当然，也仅仅在这个时候，人们才可以真正地说，量子力学的哲学基础得到了成功的构建。

       其实，也仅仅在这个意义上，人们需要意识到，整个自然科学体系本质上是一个不可分割的整体。因此，没有对现代自然科学体系一种整体意义上的了解，没有对于前人在构造不同理论体系的历史性过程中某些思维细节、目的、困难和可能存在的不足有所充分认识，对于自然科学中长期存在的一系列任何重大难题的解决终将成为一句空话。当然，对于自然科学研究中“逻辑自洽性”和“物质第一性”两个基本原则相互依赖的共存关系，也难以形成一种真正理性的认识。

       包括变形体力学、流体力学以及热力学在内的整个宏观力学，属于现代自然科学体系中历史最为悠久的研究范畴。它们的研究对象都是一些被称为“宏观物质”的大数粒子所构造的物质集合。于是，从形式逻辑考虑，在粒子系统的“离散”本质，与粒子系统宏观表象通常总借助于微分方程加以表述的“连续性”形式特征之间，必然存在某种具有根本意义的矛盾。事实上，正是这种形式表述上存在的矛盾，以及如何在这样两种具有本质差异的形式表述之间构造一种逻辑关联方面缺乏理性认识，制约着整个宏观力学体系。其实，人们总可以相信，对于所有源于粒子集合的宏观物质的宏观表象，为某一个形式系统所描述的连续特征必然只是条件存在，而离散恰恰是本质的。

       事实上，如果人们真正意识到宏观物质的粒子本质，并且，能够把“湍流”认定为源于这种粒子本质而出现不同特定“流动结构”的一种复合，那么，对于流体运动过程中不同流动结构的形式认定以及对这些流动结构所表现物理内涵的确切描述对于理性地认识湍流将具有根本的意义。从物质本原考虑，既然变形体和流体本质上都是大数粒子构造的宏观物质集合，那么，变形和流动必然可以互为转化。因此，人们可以逻辑地确信：作为大数粒子集合的流体在进行本质上以“相互滑移”为基本特征的流动过程，同时可能发生局部域中存在的变形。那么，在原则上，这种流动过程中实际出现的局部变形，与为人们所熟知的变形体在变形过程中由于局部域流动而出现不同形式的断裂面或滑移面，即塑性变形并没有任何本质意义上的差异。事实上，对于宏观力学中人们通常所说的两种不同物质存在形式以及相应出现的“复杂运动”而言，不同特征的宏观间断面将成为它们共同具备的抽象同一性。反之，人们也可以把出现不同形式“宏观间断”现象的变形以及流动，统称为宏观物质的“复杂运动”。

       因此，一旦意识到宏观物质的粒子本质，宏观物质出现变形和流动并存的复杂运动，恰恰应该被视为一种正常。相反，以保持粒子系统中存在确定性相邻结构为前提的“纯粹变形”，以及以相邻粒子之间的滑移为基本特征的“纯粹流动”，只能是两种条件存在的运动形式。也正是在这个意义上，人们应该相信，任何一种为经验事实所验证的“存在形式”和“运动形式”都必须被视为一种正常。如果这些真实的存在一旦在与人们的认识之间出现了矛盾，那么，这种矛盾只能源于人们自身认识中存在的反常。

       反观整个宏观力学，虽然为宏观物质的“变形”运动和一般的“流动”现象构造了不同的形式表述体系，但是，恰恰在“变形”和“流动”这两个前提性概念上缺乏明确的界定。特别是，上个世纪的理性力学家试图以“与数学上的Euclid空间保持同构的连续介质假设”为宏观物质的“同一化”物质模型，从而为整个宏观物质的运动构造一个本质上“同一化”的形式体系之时，连“变形”的“流动”之间曾经为人们大概确认的形式差异也不复存在，而被统一地代之以一个“同一化”的称谓：宏观物质质点在满足“连续性公理”假设前提下的“许可运动(permissible motion)”。如果按照在这个领域曾经发表了大量著述的A. C. Eringen在《连续统力学(Mechanics of continua)》一书中的诠释，“连续性公理(Continuous axiom)”又可以被极其形象地称之为“不可切入公理(Impenetrability axiom)”，它表明这样一种基本事实：运动使每个区域变成一个区域，每个曲面变成一个曲面，每条曲线变成一条曲线，物质的一部分绝对不会进入到另一部分中去。“连续性公理”是整个现代连续介质力学赖以存在的基础，恰恰是对于“连续性公理”所作的这样一种极其生动的解释告诉人们：这个必须的普遍性前提是完全不真实的。当然，在这样一个完全有悖物理真实的形式系统之中，人们根本不可能理解和描述宏观物质所作的复杂运动。

       同样，人们还可以确信：对于以宏观表象存在某种抽象形式间断为基本特征的复杂变形和复杂流动，其根源绝对不在于为人们所构造的某一个形式系统的所谓“非线性”特征，也不在于需要服从人为制定、以连续可微作为逻辑前提的所谓“分支理论”。任何形式系统都是人为构造的，这种构造应该服从于其描述的物理真实，而这种物理真实同样需要服从于其真实蕴含的物质内涵。如果人们缺乏一种能力，能够对被描述的物质对象做出一种“合理”的认定，也就是说，对于“物质对象”中某种人们希望描述的“局部真实”能够相应构造一种基本一致的理想化假设，相反，却将某一个永远只能“条件存在、有限真实”的形式系统视为某一类物理真实得以存在的导因，不能不视为一种极为幼稚和浮浅的认识反常。然而，这种反常极其严重地存在于整个现代自然科学体系之中。并且，正是这种认识反常的长期存在，使得当今自然科学体系至今无法抛弃那个人们早已意识到没有任何逻辑内涵、仅仅依赖于循环定义而得以存在的“惯性系”；无法理性地接受“Michelson-Morley实验”所揭示的真实实验结果；无法理解“湍流”；无法排除“经典热力学”中一系列为“现代理性力学家”已经指出的大量“数学和物理概念的紊乱以及由此引起的神秘性”问题；当然，也永远不可能为“量子力学”真正建立一个真正可信的哲学基础。

        可以相信，即使仅仅从形式逻辑考虑，对于自然科学的一切形式表述系统，那个被描述的物质对象必须具有前提性的地位。宏观物质是粒子的。因此，宏观物质运动中展现出现种种复杂性只能是宏观物质粒子本质的逻辑必然。处于复杂外部条件下的大数粒子集合，无须也不可能始终按照某一个形式体系中所蕴含的某种人为愿望，去实现属于宏观物质自己的运动。事实上，本质上作为粒子集合的宏观物质以一种最有效的形式实现属于自身运动，是宏观物质运动一切复杂宏观表象中最为本质的内涵。人们没有任何理由，要求这些几乎难以计数的粒子共同构造的物质集合，服从某一个一成不变方程，以某种人们某种过分幼稚的期待。在自然科学研究中，无论某一个特定的形式系统在数学上如何复杂，但是，与被描述的物质对象相比，它总是简单、有限真实和条件存在的。

       也正因为此，人们可以断言，目前的整个自然科学体系普遍存在一种极其扭曲的认识反常：当人们希望构造一个所谓的“公理化假设下的形式表述系统”时，那个公理化假设通常并不是对于被描述的物质对象做出的前提性理想化认定，相反，在无视特定的理想化物质对象和形式系统的有限论域的同时，人们习惯于以若干本质上仅仅条件存在、附属于特定理想化物质对象之上的关系式作为构造某一个理论体系的唯一前提，进而在此基础上进行根本不讲究逻辑严谨性的“无穷演绎”。事实上，正是对于形式表述可能蕴含的某种普遍意义的过分期待和刻意追求，与此同时，却表现出对形式表述自身逻辑内涵的随意性，人们不得不长期地容忍Newton经典力学体系中的“惯性力”对于这个理论体系得以存在的逻辑前提所构成的一种逻辑否定；甚至容忍年轻的Einstein仅仅凭借一种直觉和对于Spinoza理想的一种真诚信仰，将一对“矛盾着的真实”认定为全部形式推理的基础，本质上借助于改变形式语言的逻辑内涵以构造一个能够对无尽的物质世界做出某种“同一化”描述的“世界图” ¼…

       如果说，现代理性力学家已经充分意识到宏观物质的粒子本质，只是尚没有能力将宏观物质自身蕴含的“离散特征”和相关形式系统需要的“连续性前提”如何构成一种恰当的逻辑关联，那么，对于为现代理性力学家所期待针对宏观物理学所作的理性重建，它得以实现的全部基础只能在于将这个至今没有完成的前提性工作重新提到议事日程之上。

       任何一个诚实的自然科学研究者必须自觉地承认，研究者个体的认识能力总十分有限。对于认识的重新认识的过程，不仅首先包容对于经典认识的深刻理解过程，同时也自然地包括认识者个体对于自身认识的不断反省和深化。认识的深化依赖对于认识深化过程中的反复认识和批判。因此，当人们面对的是“湍流”等这样一些世纪性的重大论题时，笔者格外渴望和珍惜与许多专业研究人员以及立志于探求真理研究者进行深入交流。同时，笔者也深深感谢国家自然科学基金委员会一些热心祖国自然科学事业的同志们曾经提出召开一次国际学术研讨会的建议，虽然现在看来真正能够召开这样一次拟议中的学术交流机会并不容易，但是，这个建议却在事实上迫使我进行了又一次深刻反省自我认识的机会。事实上，本书正是在这样一个特定的背景下得以开始和完成的。

       变形体和流体都是宏观物质，宏观物质的变形和流动不能决然分开。因此，变形体力学和流体力学不仅存在着形式意义的交叉，而且，正是许多特定场合下宏观物质变形过程中可能出现局部域的流动，以及流动过程几乎普遍存在的局部域变形，使得整个宏观物质的运动复杂化了。在这个意义上，人们无法将变形体力学和流体力学，以至这两门学科共同需要的基础，热力学理论体系完全分开。但是，必须指出的是，此书并不属于论述整个宏观物理学的一部完整教程。事实上，当人们在理论物理中这个庞大领域中的许多认识尚没有真正达成一致以前，需要以如何解决“湍流”疑难为中心，对于存在于“宏观力学”、“经典热力学”乃至“统计力学”中的基元概念与一系列彼此相关的问题进行一种整体意义上的分析和重新认识。

       因此，不是严格按照建立一个理论体系的基本思维脉络，而是根据人们可能大概感兴趣的程度或者宏观物理学中许多前提性的概念，首先将一些不同的论题汇编成以《宏观力学基础分析—— 宏观物理学哲学和数学反思》”为总题的三卷，它们分别是

       卷1：湍流及理论流体力学的理性重构

       卷2：宏观物质粒子本质和热力学理性重建

       卷3：宏观力学若干基本概念的澄清

随着这种探讨的不断深入，笔者的确心存这样一种期待：一个更符合一般书写特征的后续各卷可能得以继续出版，虽然这些后续的篇章无须也不一定能够出自笔者之手了。当然，一个更为恰当的说法应该是：一系列必要的进一步论述，需要由许多更富朝气和更具科学批判精神的年轻学者加以完成。其实，在古老的中华大地上，曾经涌现过震撼世界的灿烂文明，仅仅由于历史的原因，在现代自然科学基础的“体系性”构造上几乎没有中国人的痕迹。因此，切实鼓励和崇尚科学求实和科学批判的精神，重新塑造具有独立思维能力的科学研究群体，更是笔者许多年深藏内心的一种更为真诚和强烈愿望。

       在目前初步拟定的三卷论著中，第二卷的初稿也已基本完成，而第三卷只是构造了一个书写大纲。尽管所有的论述本质上彼此关联，但是每一卷乃至每一章都能较为集中地讨论某一个领域的问题，甚至某一个特定的论题。这样，相对而言，希望能够达到一种目的：对于科学哲学、应用数学、理论物理以及宏观力学等不同领域中的研究者，或许可以仅仅针对他们特别关注的论题进行较为独立和完整的思考，并且提供一种做出大概判断的可能，对不同的独立结论给予一种较为明确的肯定或者否定。这样，不妨将本书称之为一本“论文集”，或许更为合适一些。

       尽管如此，完全按照按最初建议，将一些基本观点整理成为便于专业研究者阅读的小文章的要求，现在看来并不十分容易实现。以往在不同的场合，笔者曾经多次表达这样一种观点：在自然科学体系中，许多问题之所以长时间没有解决，其根本原因主要在于现代自然科学体系的划分过于细致，以及许多研究者个体迫于社会压力对于研究成果一种过于急切的期待，以至于无力进行一种整体意义上的深刻思考。其实，真正的科学陈述始终应该是简单和自然的，容易为人们所接受。对于自然科学以及对科学研究者个体的任何神化，只能将科学引入歧途。几乎不存任何例外，在自然科学的发展过程中，每一个科学研究者的思想或者基本思维模式只能历史地决定于那个时代的认识水平。因此，将许多必需从整体意义和历史层面上进行的反思被刻意地重新打散，或许成为一种新的本末倒置。可以坚信，如果期望做出真正具有独立意义的研究，解决长时间积淀下来的一系列重大科学难题，那么，必需在每一个基元概念以及科学体系的整体上进行深刻思考，并且为此付出艰辛的劳动。

       当然，对于任何一种严肃的科学批判，必然首先包含讨论命题的确定、不同认识歧义的揭示以及相关分析，以至最终达致共识的过程。在自然科学研究中，认识歧义的存在是正常的。但是，无视歧义的存在，拒绝批判，回避对于认识歧义进行公开、理性、深刻的分析，则是一种反常。事实上，对于以物质存在为研究对象的自然科学，能够使人们达成共识的基础就是一切科学陈述必须的逻辑自洽性。

       正因为此，当如此长时间地面临自然科学中存在的某些重大问题，人们不得不使用具有确定意义的形式语言，对经典理论中的基本概念、基本方程给予重新逻辑认定，并且，在此基础重新构建相关理论体系。对基础理论中基元概念的重新界定，乃至对相关基本方程和理论体系的重新构造，对于每一个诚实的科学工作者都是无可回避的大是大非问题。在这种大是大非问题面前，回答科学批判的唯一方式，仍然是采用科学语言所进行的科学批判。人类的认识总是在“承继性的批判和批判性的继承”过程中逐步得以深化的。为了便于不同相关领域中的研究者进行较为深刻交流、探讨以及对于认识过程中仍然存在的不足进行批判，尽可能使得针对不同论题所进行论述存在一定程度的独立性，同时，也有意识地适当保持笔者在认识深化过程中曾经真实存在的思维痕迹。

       随便指出，普遍存在于当今整个科学世界，对某些“智者(Sophist)”的“直觉与顿悟(Intuition and insight)”一种过分的渲染，都是整个人类的一种悲剧。无论是对于“智者”过度崇拜的普通人，还是对一些“过分欣喜于自我智慧”的自得者，以及“只是无奈地被他人推至这个高位”的科学工作者而言，其实是同样可悲的。如果说，许多科学史研究者往往习惯于将Einstein的一生称之为一种悲剧，那么可以相信，这种悲剧并不简单源于“构造统一场论”没有获得成功。Einstein生前多次发表了对于形形色色吹捧的极大愤慨。从中不难大概推断，正是这种将其置于“常人”之上的无奈，使得诚实的Einstein不得不忍受一般人或许无法感受到的极大痛苦。也正因为此，和那些沾沾自喜于一得之功者相比，Einstein无疑成为一个值得人们永远敬重科学研究者。

       当然，从另一个角度考虑，现代自然科学体系中对于个人所作的过分渲染，同样对应于一个真实的存在基础：这就是目前的自然科学体系的确大量真实地存在着“不可思议”的未知现象。事实上，也仅仅由于对这些“不可思议”的存在所表现的一种完全无为的状态，上个世纪的物理学世界才可能容忍和默认年轻的Einstein以一对“真实存在、然而‘不可也不允许解释’的矛盾真实”作为构建他的理论体系的全部基础，并且，接受以“对形式语言的语义加以‘改造’”为本质内涵的“时空观”革命。自然，作为这样一种理念的逻辑必然，现代的整个自然科学，必须依赖隶属于某些“先知(Sage seer)”的一种纯粹“先验（transcendental）”的智慧而得以存在，反对任何“凡人”对于这种认知所作的任何形式的批判。在这个意义上，无论诚实的Einstein怎样厌恶人们对于他个人的神化，但是，仅仅依赖于“直觉和顿悟”而得以建立的“相对论”，只能将他推向“神”的位置。

       20世纪中，伴随于人类对于其生存的物质世界形成愈益深刻认识的同时，“神学”被人们“自觉和不自觉”地重新引入了“现代自然科学体系”。如果说，这种现象可以被视为20世纪自然科学发展过程一种十分奇特的现象，那么，人们同样需要意识到这种现象得以存在的某种必然。事实上，当著名的物理学家Landau十分诚实地将“理论物理中的数学严谨性”称之为“自欺欺人”的时候，现代科学主流社会的许多“科学家”只能借助于那种不可解释的“宗教情结”，让人们仅仅以一种“纯粹信仰”的方式接受以“相对论”为基础的现代自然科学体系。此处，不妨引用Nobel奖获得者，杨振宁教授关于“科学和宗教”之间的一段为许多当代中国学者熟悉的论述：

       “关于科学和宗教的问题，是一个很重要的问题。一个科学家做研究工作的时候，当他发现到，有一些非常之奇妙的自然界的现象，当他发现到，有许多可以说是不可思议的美丽的自然结构，我想，应该描述的方法是，他会有一个触及灵魂的震动。因为，当他认识到，自然的结构有这么多的不可思议的奥妙，这个时候的感觉，我想是和最真诚的宗教信仰很接近的。所以你问：相信不相信在不可知的宇宙中有造物主在创造一切吗？这个话，我想我很难正面回答是或者不是。我只能说，当我们越来越多地了解自然界一些美妙的不可思议的结构后，不管我们是正面问这个问题还是不正面问这个问题，都确实有你问的这个问题存在。是不是有人或者有神在那里主持着？这也是一个永远不能最后回答的问题。”

       如果说，对于杨振宁先生此处所说的“奇妙的自然现象”或者“不可思议的美丽的自然结构”，如果人们能够理解为是人类对于物质世界“无以穷尽的存在形式和运动形式”，以及这些不同存在形式通常蕴含的一种“共性规律”而引起的感叹，那么，人们可以确信：这种共性规律只能同一于理论物理中那个普遍存在的“最小作用原理”。并且，如果仅仅局限于“自然科学研究”的范畴以内，这个原理其实也仅仅是“自存的物质世界必然独立于任何‘人’或者‘神’的意志，以一种‘最有效的运动形式’实现属于自己运动”的逻辑必然，根本无法成为某种“超自然意志”的佐证。至于说，如果将这种奇妙性归结为Einstein经常所说的那个“在‘秩序’和‘和谐’中显现出来的Spinoza上帝”，乃至更加具体化到某一个非常“美妙”的数学表示形式，则恰恰构成对于“物质世界多样性”的逻辑否定。因此，这种感叹如果成为希望人们对这个特定的数学表述表示一种“不加批判的纯粹宗教式”的认同，则完全不当。

       与杨振宁先生同时荣获Nobel奖的李政道先生，近年来曾经多次向人们提出“物质世界中非对称性与物理世界中对称性之间矛盾”的问题，并且，将这样一种真实存在称之为“21世纪的第一科学难题”。因此，起码像人们已经看到的那样：对于“无尽的物质世界”本身，是根本无简单的“秩序”和“和谐”可言的。更为恰当地说，物质世界真实展现的复杂性，恰恰是物质世界自身多样性的逻辑必然。因此，在这个意义上，对于某些自称为Einstein承继者的当代智者，提出用一个“12维的壳（流形）”取代Einstein最初的4维Riemann空间，那么，从宗教的角度考虑，这种取代仍然无异于一种“背叛”，而从科学研究的哲学理念考虑，两种数学表述之间没有任何本质差异。显然，对于那个无尽的物质世界，这个12维的壳仍然显得过分简单。因此，除了“神”的意志，大自然没有必要服从这样一个过分简单和单调的形式表述。而且，如果日后又出现另一位更为聪慧的智者，他提出需要用更高维数的抽象空间取代这个12 维的壳，我们的后人又将如何处置呢？

       事实上，如果说贯串于Einstein毕生科学研究之中，自始至终表现了对于“秩序”和“和谐”的一种真诚追求，那么，这个期待之中“秩序”和“和谐”的全部逻辑内涵，需要也只能仅仅表现在“自然科学体系”以内：表现在对于形式语言一种绝对的“无歧义”认定之上，以及表现在一切科学陈述之间的“严格无矛盾”之中。

       其实，如果反观整个自然科学体系，人们至今并没有真正说出任何比物质世界自身存在更多的东西，也没有人们期待中的那个“因果规律”。进一步说，赋予人类整个自然科学事业的使命，也仅仅在于如何能够“无矛盾”地揭示存在于“物质世界自身”蕴含的某种抽象同一性。反之，只是因为某些物质对象自身存在的抽象同一性，它们才可能共同遵循某一个相同的“形式规则”。在这个意义上，“逻辑自洽性”不仅成为一切科学陈述必须遵循的基本原则，同时还揭示了自然科学中“可解释性”的真正本质内涵。而且，自然科学必须遵守的逻辑自洽性原则，还将成为解决自然科学中一系列世纪性重大难题的唯一武器。相反，如果公然无视物理学陈述中的数学严谨性，如果背离了“逻辑自洽性”的必要前提，原则上已经没有自然科学可言，也根本无“秩序”和“和谐”可言，恰恰成为对于Einstein理念的一种逻辑否定。

       在这个意义上，对于Einstein所生活的那个时代中信奉他所构造的“相对论”的科学主流社会，与Einstein本人之间长期存在的旷日持久的争论，无论是从社会学的角度考虑，还是从纯粹自然科学研究的角度考虑，都远没有结束。一些科学哲学家指出：“学术机构的门户之见，学派之间的意气之争，专业团体对外行的排斥，总之，科学界中的宗派倾向，常常导致对科学发现的抵制。”或许，还应该包括“科学研究同样仅仅属于‘人类社会生活’一个部分”的这样一种客观真实，使得当代的科学主流社会，甚至在面临形形色色“超光速和亚光速”现象被实验确认，从而本质上动摇了整个“相对论”得以存在的全部基础的时候，仍然不愿意接受真诚的Einstein去世前一再提出“需要不时对整个物理学体系加以反思”的忠告的原因。可以坚信，无论人类的历史怎样发展，人们最终仍然无法回避如何给予Michelson-Morley实验一个真正理性或者符合逻辑的解释的问题。当然，这也是笔者提出努力以“逻辑自洽性”为原则，对自Newton开创的整个自然科学进行一次“历史性和全局性”梳理时，无法回避的另一个本质上属于自然科学研究以外，一个本质上属于“社会学”的重大课题。

       如果说仅仅出于对于探询真理的一种真诚和热切，笔者不自觉地步入了基础研究乃至纯粹基础科学研究的领域。那么，在这个逐步深化认识自然的过程中，对于自然科学研究中某些社会学现象存在的认识也在逐步的深刻化。历史和现实似乎都说明：科学研究中的许多困难并不真正源于科学以内，而源于科学生活中一系列正常机制没有健全。当然，尽管其间的际遇常常不能不使得笔者心怀一种苍凉或者感慨，但是，仍然值得庆幸的是，时代毕竟在进步。和历史上对经典认识提出批判的许许多多前人曾经遭受的际遇相比，笔者的确十分幸运。事实上，没有笔者所任教的上海交通大学领导极为难得和宝贵的支持，没有学术界许多善良、正直的前辈、同行的鼓励，乃至工作在不同领域中许多素不相识朋友的激励和支持，这些年的研究是难以继续下来的。当然，也正因为此，笔者对于他们，对于他们曾经给予的真诚支持，甚至为此而同样承受着的同样压力，表示深深的歉意和由衷的感激之情。

       科学是属于整个人类的。但是，毋庸讳言，对于整个现代自然科学体系的构建，西方人曾经做出了比东方人更多的历史性贡献。因此，如果像许多东方研究者往往容易感受到的那样，个别西方学者在“彬彬有礼”的仪表之下，常常会不经意间表现了一种特别的优越感，或者也可以称之为一种“过度自信”与“思维优势”吧，那么可以说，这样的行为仍然可以认为是不难理解的，相应具备一个真实的“存在”基础。包括Einstein在内的许多西方学者，曾经批评东方科学在“形式逻辑”方面的不足，相对而言，更长于“辩证逻辑”。但是，如果对照Mach严厉批判“相对论”时曾经指出的“过分形而上学”，那么，人们可能更需要意识到，如果无视“矛盾”存在，完全不在乎“数学严谨性”而构造的“形而上学”表述，不仅是对“形式逻辑”自身的一种简单化，而且，它还像人们已经看到的那样，本质上构成了对于以“逻辑自洽性”为中心的“形式逻辑”的一种根本否定。其实，恰恰从“形式逻辑”考虑，这种建立在“过分形而上学”之上的简单化，正是现代整个自然科学体系至今无法从以“循环逻辑”为基础的“惯性系”等一系列重大的“逻辑悖论”之中解脱出来的根本原因之一。

       因此，姑且人们不必认真理会西方学者对于“东方思维”的这种评价是否足够准确，但是，当目前仍然为西方学者占据主导地位的现代科学主流社会，长时间面临着一系列的历史性重大科学难题无法解决，乃至不得不“公然或者隐晦”地声称需要放弃自然科学研究中的以“逻辑自洽性”为根本内涵的“理性”原则的同时，却几乎公然拒绝对于这个理论体系一切严肃的、带有根本性意义的批判的时候，整个科学世界或许需要共同意识到：如果在自然科学研究中能够相对更多地融入“辩证逻辑”中的一种“整体意识（对立的辩证关联与统一）”，乃至或许为东方民族所具备的一种相对更为细致的思维习惯，那么，它们将成为东西方民族对于人类科学事业的共同贡献。

       由于历史的原因，在当代自然科学“体系性的研究和建树”中，几乎没有任何真正属于中国人的痕迹。至今，中国乃至国外华人学者在基础科学上的研究，仍然大体上属于一种“尾随研究”的范畴。对于曾经拥有古老文明的中华民族，这的确是一个不愿意接受的事实。然而，恰恰为了改变历史，对于每一个炎黄子孙，不仅需要正视这种存在的真实性，而且，还需要充分警惕和彻底根除同样由于历史的原因，而潜藏于许多中国人内心深处一种属于“殖民地和半殖民地”民众的“无为”意识。当自然科学体系仍然存在大量的世纪性难题时，对于Nobel奖一种“有意识或者无意识”的过分渲染，除了损伤一个自尊的民族满足必须拥有的自信心以外，没有任何意义。可以相信，在世纪性世界难题面前，没有任何权威可言。因此，破除迷信，真正树立自然科学研究中必须进行独立思考的意识，崇尚使用科学语言进行真正科学意义上的科学研究和科学批判，对于中国独立的自然科学研究体系的建立具有前提性的根本意义。也仅仅于此，中华民族才可能再次赢得整个世界的尊重，中国的自然科学研究才可能真正步入世界科学的发展进程，自立于世界科学之林。

       真正科学的，必然是自然的，容易为人们所接受。在自然科学研究中，允许，并且切实鼓励不同学术观点之间采用“严格科学语言”进行的争论，是科学得以存在的核心内涵，同时，也是科学得以继续发展，不至于重新陷入宗教的唯一途径。科学属于人类，属于历史发展过程中的整个人类。在自然科学“承继性批判和批判性继承”的发展历程中，对于物质不同“存在形式和运动形式”的揭示始终具有前提性的根本意义，并且，也相应决定了那个“时代”的认识水平。从这个意义上讲，Einstein的出现以及对于Einstein“相对论”的重新认识，同样都是自然的。可以相信，出现于研究者之间的不同意识，或许同样需要被视为人类认识历史进程中的一种必然。也同样在这个意义上，人们可以说，某一个研究者个体的认识，对于整个人类认识的进程始终微不足道。因此，在人类深化自身认识的过程中，昭示深化认识过程某些真实存在的不足，将永远比简单陈述一些最终的结果更为重要。为此，人们需要重新召唤科学赖以生存和发展的科学批判精神，而笔者愿意充当科学批判中的一只“靶子”，奉献一份微薄然而真诚的力量。

杨本洛

初稿于2001年5月，9月略作增删 [1]

Persistence of material primary and logic consistence principles in natural science

Overall preface to

Analysis on the fundamental of macroscopic mechanics - Philosophical and mathematical reflection macroscopic physics

       The turbulence puzzle is called by the modern science world as one of the most serious trials made by the great nature to human in the intersection of centuries. It seems to be an unavoidable momentous task to every solemn researcher in the regions of theoretical fluid dynamics or the foundation of theoretical physics. However, it may be accredited to contingency for the writer to possibly make a rather deep study on such an interesting area. As a teacher or researcher initially working in the general engineering technique, the writer, being encouraged by the genuineness to investigate unknown and wanting to conform to the requirements raised in some actual works, has unconsciously stepped into such a purely fundamental researching domain, where there is full of challenge, of natural science.

       In the past few years, some monographs touching upon thermodynamics, fluid dynamics, relative theory as well as classical Newtonian mechanics, electromagnetic theory, all of which may be dealing with the different opinions on the philosophical and mathematical base of natural science, have been sequentially published. The writer tries to strictly follow the logic consistence principle necessary to all the science statements and endeavors to make a rational reanalysis on a series of primary problems in macroscopic mechanism as well as the foundation of all the theoretical physics.

       Indubitably, a lot of opinions, mentions and inferred conclusions rather greatly differ from the classical acquaintanceships accepted, supposed or maintained to the utmost by the main current science society. But, any real rationality cannot be destroyed by any rational criticism. If our classical cognition really contains of forms of contradictions and wrongs that do not have any evasive answers, the solemn criticisms based on the serious science language and aiming at the classical theory cannot but show us that the conventional knowledge system really needs to be recognized no matter how long history such knowledge may have. Of course, the recognition of cognition will be hard to avoid some new problems, insufficiencies and wrongs. Just for it, and even as known well to everybody, our natural science system is still confronted with a series of prerequisite unsolved problems: what the inertial system based upon a circle definition really is, what turbulence is, how can we understand the intrinsic conflict between the asymmetry essentially implicated in the material world and the symmetry presented in the physical world, and how can we support a reliable philosophical base for the current quantum mechanics, and etc.? So, there is no reason for our science world to refuse any criticism. Besides, only for the reveal of forms of difference or contradiction, and tolerating and promoting every solemn criticism that uses a serious mathematical language, would it be possible for people to reach a common view in a new cognition level. Affirmed, once the aspect that the classical cognition cannot be doubted is changed, a lot of puzzles existing in the natural science over centuries will be solved.

       When this spring is changing into summer, there presented an opportunity for the writer to make an initial discussion on the way how the Chinese science researches to enter the science world and occupy an independent position with some friends who work in National Natural Science Foundation and have been paid some attention to my researches. They supposed that it might be convenient and proper to hold a small-scale international proseminar to make some exchange with some researchers, which would be limited within theoretical fluid dynamics in the first, and then required me to arrange some related literatures. While my fundamental researches has been forced into a nearly closed situation for a rather loge time period, it would be rather valuable to these unfinished works and, needless to say, I would treasure it very much.

      But, in the current view, it looks as if the things worth for me to especially highly value, which may be expected or unexpected, would be: after some rethinking on macroscopic physics and having paid my attention to other realms of natural science, such as Newtonian classical mechanics, relative theory, electromagnetic theory, for a certain time interval, and remaking some reflection on the considered problems, I found the analyses and criticisms on the classical theorems made by me in these years to be far from deepness and nicety. Namely, within some most fundamental concepts, the recognition or deliberation on the conventional ideals is so insufficient that these criticisms cannot really rid of the tie of the improper classical material description, which has usually involuntarily ingrained in the mind of everybody even involving the criticizer himself.

       Correspondingly, while considering how to perfectly express the complex movement made by macroscopic material set, the writer still passed a process to make a new recognition on the initial recognition and a self-criticism on the criticism, that is, changing from the criticism on the indeterminacy presented in forms of turbulence models into the re-affirmance of such a basic character that must be implicated the particle connotation of any macroscopic material. And that, it can be logically validated that any classical laws in theoretical physics must not possess formal completeness in expressing the ‘general’ macroscopic movement. In such significance, any form of variational principle can only supply a reliable fundamental for people to generally reasonably describe the complex movement of macroscopic material. But, if lacking of some empirical countenance in some special flowing structure, the variational principle only with formal meaning cannot become as an independent calculation model. Believed, if it may be said that any time of successful deepening of cognition must need a hard process to repeatedly deepen the cognition, the rational rebuilding or reconstruction on the current macroscopic physics would be the continuation of such a progress to deepen the cognition and a lot of propositions are waited us to further research.

       And, just for it, in natural science investigation, it is needed to re-erect the rationality that takes the logic consistency as its entire kernel. Especially, while some honest and influential scientists frankly accounting the mathematical rigor presented in theoretical physics that is defined as a branch of physics written in mathematics to be as self-deception and then taking it as the reason to consciously or unconsciously sustain an ‘extreme metaphysical order’ full of forms of paradoxes, which has essentially degenerated into a science religion complex so-called by some main current scientists, it would become rather imminent and important to sincerely recall the solemn science criticism that takes the serious inter-consistency at its unique criterion.

       Natural science is only as a small part of the human knowledge system. As a positive definition accepted by almost every scholar, natural science is used to describe forms of material object existing in the great nature. Therefore, even though disregarding the argument about ‘theism and antitheism’ or ‘idealism and materialism’ and ignoring the original problem that what the material or existence really is, the specified object described by a formal system would always be at a primary position only according to the formal logic. In logic, if the object did not be endowed with some certain formal significance, the formal system describing the object would not exist either. Of course, only according to logic, it is possible for us to supply material or existence with a particular item, that is, a special cognition object. Restricted in such significance, we may even say such a too old and naïve proposition to be too simple to have any real insignificance when being faced with the boundless realm of nature full of innumerable existence and motion forms.

       Then, still based upon some most basic logic, a totally anomalous conventional cognition should be thoroughly eradicated from all the natural science system, that is, any only qualified and finite real relation or equation connecting different physical quantities defined in some idealized material object has beyond comprehension been dislocated in the primary position, which should belong to the idealized material object, from the era for Newton to create his classical mechanics. Just for the dislocation of fundamental premise, people have accustomed to make some ‘endless inference’ only from an equation while disregarding logic rigor and the qualified conditions. And it should be the reason for people to have impossibly answered what the inertial system really is, why Michelson-Morley experiment presents an identical vanishing result and how supply a believable philosophical foundation for the modern quantum mechanics.

       The realm of nature is boundless while it will always be impossible for human to either exhaust the reality of the nature or construct a unite formula for the nature. However, the language used to express the mater world must be unite and strictly unambiguous. It is unnecessary and impermissible to supply different and even conflict principle for the different parts of the mater world, such as both the distinct macroscopic world and microscopic world in appearance. Any particular formal characters can only rely upon the described material object itself or a reasonable idealization on the described material object.

       While the science main current society almost impossibly throttling forms of spontaneous criticism or reflections on irrational relative theory, an important problem lies in the fact: it is not only relative theory but also the all current natural science system beginning from the creation of Newtonian classical mechanics that neglect a primary principle how to give the described material object as well as a related idealized material environment with a positive formal definition. Of course, just for the prerequisite problem unsolved, a qualified and only finitely real formal is usually misinterpreted, as a universal and unqualified truth, no matter such an illusion is conscious or unconscious.

       In fact, while putting the belief that the whole material world must be connected by a nice, united and universal formula, namely the well-known Spinnoza idea, as his total thinking foundation and then taking both the ‘constant light velocity principle’ and ‘relative principle’, a pair of conflict realities unnecessary and impermissible to be made any interpretation, so called by himself, as the premise of his theory, the honest but too juvenile Einstein as well as all the adherents have never given any rational interpretation, which just coincides with the reality seen by everybody and, consequently, it should still be ‘unnecessary and impermissible’ to make any interpretation. Then, it becomes nothing but rather strange religion devotion popularly existing in the modern science world, which is frankly called as a science religion complex by somebody in the main current society. Provided no prejudice, it is not difficult to rationally judge, in essential, a so-called ‘space-time opinion’ revolution would aim for no more than wanting to make an identical, unvarying and universal interpretation on the nature just by changing the semantic of formal language. Certainly, it is absurd no matter how many times of empirical identification seem to be gotten. In fact, when closing the end of life, the honest, kind and great Einstein seemed conscious of a simple fact: a pair of ‘rigid ruler and proper time’, which were introduced into his theory as a united measurement standard, had put his relative theory back into the Newtonian space-time opinion in logic.

       Some originally plain verities have been demonstrated in ‘An essential analysis of natural philosophy – the philosophical and mathematical reconsideration of relativity’, which was written in a few years ago, that is: When reconsidering the classical Newton motion law, which would better be as a formal definition on force acted on a mass-point in essential as pointed by people much earlier, if all the material existences dealing with the formally defined force, a body that supports the force and a body that supplies the force, have been determined, the inertial system based on a circle definition and the indeterminacy of all the kinematic quantities, caused by innumerable inertial systems, will not still exist; At same time, once rationally understanding an inseparable re-reliable relation between an electromagnetic field and both the charge and current distributions, the later may be as the cause of the former while the former as the effect of the later, it become a rather simple and natural conclusion that the movement of electromagnetic wave appearing in the geomagnetic field should be independent of the movement of the earth and, consequently, the result shown by Michelson-Morley experiment that the velocity of ether relative to the earth is with an identical velocity also becomes as a too simple fact.

       Believed, the interpretability of the material world would never be that human can supply a reason for a real physical reality. The interpretability would lie in the abstract identity logically implicated in every abstractly identical thing or the strict logic compatibility existing among forms of science statements. And, when and only when making a generally reasonable conviction on the described material object, namely generally coinciding with the physical reality people want to express, and then correspondingly constructing a certain finite discourse universe, we can affirm that a lot of essential statements presented in quantum mechanics to be not only natural, rational and easy to be accepted but also agreeable with every rational statement in physics. Then, it is neither necessary nor permissible for us to supply a singular language system or principle for such a so-called microscopic world. Of course, in and only in this situation, it would be possible to say the philosophical foundation of quantum mechanics to be finished.

       And, in such significance, it should be conscious of that the natural science system is as an inseparable whole and, if a researcher being without a global understanding of the science system and some sufficient cognition on the thinking details, aims, difficulties and possible insufficiencies presented in the history progress to build the modern natural science system, the solution of any single important puzzle would become an empty word. And, it would be impossible for people to rationally cognize the co-existing and interdependent relation between the ‘material-primary’ and ‘logic-consistency’ principles indispensable to every science statement.

       Macroscopic mechanics involves thermodynamics, deformation body mechanics, fluid dynamics and even statistical mechanics and belongs to a realm with rather centuries-old history in the natural science system. In this realm, the studied object would be a system with a large number of particles, which is generally called as macroscopic material. Then, only based upon formal logic, would an intrinsic difference be between the discrete character implicated in particle system and the continuity premise necessary to a formal system written in differential equations. In fact, just for the existence of such a distinction and lacking of rational cognition how to build a formal relation between them, the development of all the macroscopic mechanics has been restricted in great degree. It is possibly rationally believed that, to the macroscopic representation originated from particle system, the continuity premise is only qualified while discreteness is just essential.

       Actually, if really being conscious of the particle essential of macroscopic material and accepting turbulence to be only as a complication of different flowing structures based upon the particle essential, we will naturally believe it to be with essential significance to rationally understand turbulence that different flowing structures and corresponding physical connotations should be made a proper formal conviction. Since both the deformation body and fluid are all as a macroscopic material with a large number of particles, deformation and flowing can re-exchange to each other. Then, it would be natural in logic, accompanying with a universal reality that some local flowing may present in a deformation movement of a deformation body, it is normal that moving fluid may present local deformation while making flowing, which takes ‘slip presented between neighbor fluid particles’ as its essential character. In fact, aimed at two kinds of material existence forms, as generally said in macroscopic mechanics, and the complex movement caused by them, the macroscopic interpretation, which essentially originates from the co-existence of two type of macroscopic movement, will be regarded as an identical character possessed by every complex macroscopic movement. And, inversely, provided with some macroscopic interruption, any forms of deformation or flowing would be called as a complex movement made by macroscopic material in most of situations.

       The particle essential of macroscopic material determine the co-existence and interchange of two macroscopic movement forms. And, just for it, a movement that is with the co-existence of two independent macroscopic types can be called as general while either a pure deformation that keeps the neighbor structure of particles unvarying or a pure flowing that means all neighbor particles to be at slip would be qualified existing. Then, any real existence identified by any empirical facts would be normal. If some reality contests against our consciousness, it would be our consciousness but the reality that is anomalous.

       When looking back all the macroscopic mechanics, we find that it just lacks a positive formal definition on both the elementary concepts, deformation and flowing, though the difference between both of which seems self-evident and two different formal systems used in them have been built. Especially, rational mechanics born in the middle of 20 century wants to construct an unite formal system, which is used in all the macroscopic material and bases upon a universal and purely continuous medium model that can keep isomorphic with an abstract Euclidian space, the self-evident difference existing between deformation and flowing should not be permissible. Restricted within this region, every movement made by macroscopic material should be preceded with a united calling: Permissible motion that coincides with continuous axiom. According to the words presented in ‘Mechanics of continua’ written by A. C. Eringen, who ever published many monographs in this area, continuous axiom can also be called as impenetrability axiom, which perceptively shows that a part of material would never permissibly be penetrated into any other parts. The continuous axiom is the base of all the modern continuous mechanics. And, just for the vivid interpretation on this axiom: such a necessary premise is totally false and, consequently, it is impossible for us to rationally understand and positively express the physical reality presented in forms of complex macroscopic movement only basing upon such a completely falsification model.

       Also believed, any complex macroscopic movement never originates from either nonlinear character or branch theorem, both of which are artificially constructed and need a continuously differential premise. Any construction of a formal system must coincide with the described physical realities while the physical realities should rely upon the real material connotation implicated in these physical realities. If lacking a capability to either make a reasonable conviction on the described material object or find a rational idealization assumption that can logically connect with the local reality we want to express but, inversely, taking a qualified and finite real formal system as the cause to present some physical realities, it not is anything but a too naïve and superficial cognition anomaly.

       Completely opposed to such a too conventional and old custom, in all the natural science investigations, we should use a generally rationally idealized conviction on the described material object to replace the primary conviction on some formula. Only based upon formal logic, should the formal definition of the idealized material object described by a particular formal system occupy a primary position in a formal system while any particular formula be dependent, subordinate or just as the logic necessary of the idealized conviction on the material object.

       If it may said that, though modern rational mechanics has sufficiently realized the particle essential implicated in macroscopic material, it is for lacking of a perfect method to logically connect such a discrete character with the continuously differential premise necessary to a general formal system, such an unfinished task should be replaced into the schedule and, moreover, become as the uniquely important foundation of the rational rebuilding of macroscopic physics.

       Every honest researcher would consciously admire the capability belonging to a single one to always be very limited. Any recognition on cognition not only needs a penetrating comprehension on these profound classical theorems but also involves a process of the self-reflection and self-criticism on these criticisms. Any deepening of cognition must rely upon the repeat cognition and re-criticisms on the cognition and criticisms presented in a process to deepen cognition. In fact, just for the advice to hold a proseminar, though which seems impossible at present, it forced me make a series of serious self-reflection once more on these reflections made before by me and, fortunately, finish a time of cognition saltus. Under such a particular background, the writing of this book began.

       Deformation and fluid are all as macroscopic material, both of which cannot be abstractly separated. Then, in deformation body mechanics and fluid dynamics, there are some intercrosses in formal. Besides, just for some local flowing to possibly present in deformation movement while some local deformation to almost universally present over a fluid field, the movement made by macroscopic material becomes more complex. In such significance, it is impossible to either divide deformation body mechanics and fluid dynamics or separate both of them from classical thermodynamics, which is as a common foundation of all the macroscopic mechanics. However, this book cannot be regarded as a complete study course about macroscopic mechanics but only aim for supplying with a principle or fundamental method to how properly formally express such a particular material object. Affirmed, while turbulence still being as a problem puzzling modern science world and before people’s cognition about macroscopic physics really reaching agreeable, a series of elementary concepts existing in macroscopic mechanics, classical thermodynamics as well as statistical mechanics need us to make a reflection through and through.

       Then, it is not following a general thinking skeleton to build a theory system but according to some detached propositions that deal with primary concepts of all the macroscopic physics, in which people may be interested in different degrees, the book nominated with a total name  ‘Analysis on the fundamental of macroscopic mechanics – philosophical and mathematical reflection on macroscopic physics’ is temporarily divided into three volumes, which are as

       Volume 1: Turbulence and reconstruction of theoretical fluid dynamics

       Volume 2: Particle essential of macroscopic material and rational rebuilding of thermodynamics

       Volume 3: Clarification on elementary concepts in classical mechanical mechanics

Along with the deepening of such a discussion, the writer has such an expectation: the succeed volumes that more coincide with the general writing ruler will be further published, though which neither need nor can be produced by the writer myself. Of course, a more exact parlance should be that a series of necessary and deeper demonstrations have to be worked by a group of younger researchers who have more vivacity and full of stronger science criticism spirit. Actually, it has been an honest and fervent desire hidden in the inner heart: The population who exhibit really independent thinking capabilities will erect in the old mother land of China, where there ever presented an avalanche of glitter civilizations, to change the situation that nearly no imprint made by Chinese in the systematic building of any fundamental theory in current natural science for the historical reason.

       In the initially studied out three volumes, the initial manuscript of second volume has been finished while a writing outline used in the third volume has been worked out. In essential, all the demonstration on these different propositions cannot be separated. But, each volume and even each chapter is almost focused on a finite region or to a special proposition. Then, it may supply a possibility for a researcher working in a professional discipline, such as science philosophy, applied mathematics, theoretical physics and macroscopic mechanics, to only study a single proposition interested to them, then to make a relative complete thinking and, in final, to probably form a general judge, namely, give a positive or negative referee on some independent conclusions. So, it might better be called as colloquia of theses.

       On other hand, such an arrangement seems to still not satisfy with the initial requirements supposed by the proposal proseminar: different fundamental conclusions or opinions should be arranged as a series of independent essays for the convenience for some professional investigators to read. It is not easy to really reach such a requirement in principle. In many particular cases, the writer ever times without number expressed such an opinion: An ultimate reason for a lot of fundamental problems existing in natural science system to have not been solved for a so long time would lie in the fact that modern science system is divided too dispersal or trivial while the heavy society pressure for an impatient expectation to work out some results incapacitates a lot of researchers from making a global examination and deep thinking on the whole of a natural science system. Any different tiny insufficiencies presented in different single branches might gather out some strict paradoxes. In fact, any real scientific must be simple and natural, and easy to be rationally accepted by people. Any apotheoses of natural science or some single researchers must lead science up the garden. Almost without any exception, accompanying the development of natural science, the main opinions or basic thinking models of each researcher can only historically rely upon the cognition level of the era. Then, the re-division of a thinking that ought to have been with a global and historical consideration cannot but be regarded an inversion that the first and last turned around. If really wanting to make some independent investigation or solve some important science puzzles settled in a very loge time, we have to make a deep and global deliberation on each elementary concept and, for which, pay rather hard labor.

       Of course, any solemn science criticism must engage such a process: the determination of a proposition to be positively studied, the reveal of cognition ambiguity and a related demonstration, and in final getting a common view. In natural science investigation, the existence of forms of cognition ambiguity is normal. However, it is anomaly to disregard ambiguity, to refuse criticism and blench before any open, rational and serious argument that uses an unambiguous science language. And, in the natural science that takes the empirical material realities as its studied object and also as its existence foundation, the unique criterion for people to possibly get a common view would be nothing but the logic consistency necessary to any possibly called science statement.

       Just for it, while all the natural science system being with a lot of unsolved basic problems, people cannot but use a united formal language to make a re-conviction on a series of related elementary concepts, fundamental equations and, as a natural consequence, to build a new theory system. Obviously, to every honest science researcher, it is an unavoidable cardinal issue of right and wrong to redefine a series of elementary concepts and, based upon which, to rebuild the related fundamental equations as well as the theory system itself. Before such a major principle matter, the unique method to answer any science criticism is still science criticisms. Any deepening of human cognition is always achieved in the process with ‘successive criticism and critical succession’. Only for the convenience for researchers working in different areas to make some deeper academic exchange and some further criticisms on some insufficiencies or wrongs existing in the process to make a reflection, would some thinking traces really appearing in these reconsideration be intentionally kept.

       By the way, the excessive romance or ostentation on ‘intuition and insight’ belonging to some sophists might be called as a tragedy to all the human, either these kind persons to devoutly worship science or both the self-congratulators for their own bright wisdoms and the workers who cannot help but accept such a high positions against their wills. If some science historians are accustomed to call the life of Einstein as a tragedy, believed, it should not simply originate from the unsuccessfulness for Einstein to construct his united field theory. Before the death, Einstein ever many times showed his indignation and heavy obligation for him to be placed higher than an ordinary person, which might be beyond the public experience. Just for it, comparing with the persons feeling self-satisfied over just a minor success, Einstein will ever be a great person whom for people to always hold respect in.

       From another viewpoint, the extreme exaggeration of individual action or brightness is also supplied with a real existence foundation, that is, there are a lot of inconceivable phenomena presented in modern natural science system. In fact, just for an utter do-nothing state while being confronting these seemingly irrational existences, the science world of last century could not but tolerant and acquiesce in the peculiar anomaly for the too young Einstein to create his theorem only based upon a pair of real but uninterpretable existences and, in final, accept the so-called ‘space-time opinion revolution’ that essentially takes the variation of language as its total connotation. Certainly, as the logic necessary of such an idea, all the modern natural science system should base upon some transcendental brightness only belonging to some sage seers and strictly reject any criticism supposed by common persons. As it is, the relative theorem based upon both the intuition and insight must put the honest Einstein into the position originally belonging to ‘God’ no matter for whom to how detest such an exaggeration.

       In the 20 century, accompanied with human’s cognition on material world being more and more deepening, theology was consciously or unconsciously reintroduced into modern natural science system. If it may be called as a very strange phenomenon presented in the 20 century, we should realize the necessary of such an existence. In fact, while Landau, a famous physicist in 20 century and a Noble Laureate, ever rather frankly accounted ‘mathematical rigor’ in theoretical physics, which is defined as the physics written by mathematics, to ‘self-deception’ in his influent physical course, the main current society of modern science can only recur to the uninterpretable religion-complex that makes people accept the modern natural science system based upon relative theorem in a pure belief method. In this case, it might as well for us to quote the words influential to Chinese scholars, made by professor C. N. Yang, who ever honored with Nobel Prize:

       ‘Question about science and religion is as a very important problem. When one scientist working, once finding a very wonderful phenomenon presented in the great nature, detecting some unimaginable and fair natural structures, I think, the unique proper method to describe such a particular emotion would be a heart-shaking concussion. And, I think, the feeling in this time must be very close to a most devotional religion belief for cognizing so many mysterious marvels to present in the realm of nature. So, to the inquiry if the architect really creates everything in the universe, I thought, it may be improper to answer yes or not in positive. The unique words for me to possibly answer would be that the inquiry itself is real. Perhaps, it is a problem without any final answer whether there is a person or God who dominates the world.’

       These veiled words are undoubtedly inspirational. However, if both the ‘wonderful phenomena’ and ‘unimaginable and fair natural structures’ maybe understood as the eulogy upon the boundless existence and motion forms of the material world and a common law strangely implicated in these distinct forms, I thought, it is just the least action principle universally existing in the physics. And that, if restricted with the realm of natural science investigation, it might be affirmed, the law is no more than a logic necessary of the independence of people’s or God’s ideal possessed by the existing-in-itself material world, that is, the material world must take a most effective form to realize the movement belonging to the material world itself. Of course, the law can never provide a proof for any super-nature. As for if such a marvel may be attributed into ‘Spinoza’s God to show both the order and accord’, usually said by Einstein, and even a very nice formula, sincerely expected by Einstein, it just supplies a logic negation against the multiformity of material world. Therefore, provided the eulogy to be regarded as a purely religious identification on a particular mathematical expression to impermissibly to make any criticism, such cognition would completely improper.

       In resent years, professor TS. D. Lee, who wined same Nobel Prize together with Yang, repeatedly supposed a paradox problem between ‘asymmetry presented in material world and symmetry existing in physics world’, and even called it as the first puzzle the science world will be confronted with in 21 century. Then, as if seen by people, it is far from ‘order and accord’ for us to consider the boundless material world. More exactly speaking, the complexity really presented in material world is just as the logic consequence of the multiformity possessed by the material world itself. In such significance, when some modern sage, who claims to be as a fair successor of Einstein, supposing a 12-dim shell, manifold, to replace the 4-dim Riemannian space initially presented in relative theory, it is nothing but a ‘betray’ in religion viewpoint or the essential identity of the initial space in the view of science idea. However, while a 12-dim shell being still too simple to express the boundless nature, a prerequisite inquiry would lie in why should the boundless nature submit such a too simple model? Besides, if a much wiser sage will present in the further, would the 12-dim shell be replaced by another more complex manifold, and then how will our successors arrange?

       Actually, if it may be said that, throughout the lifetime science investigation, Einstein had shown an honest expectation for the order and accord, the uniquely proper connotation implicated in both of them would be restricted within the inner of natural science system and lie in the strict conviction of the unambiguity of formal language as well as the absolute non-contradiction principle obeyed by all different science statements.

       If taking a panoramic view of the whole natural science system, we can confirm that neither anything more than the existence of the material world itself nor any expected causality are really found. Further speaking, the task fell on the natural science investigation would lie in how to non-contradictorily reveal the abstract identity implicated in the material world itself. Inversely, just for the abstract identity existing in a class of abstractly identical things, all of them can follow an identical formal law. Then, ‘logical consistence’ not only becomes as the basic ruler necessary to every science statement but also demonstrates the essential connotation of the interpretation of natural science. Furthermore, the logic consistence principle can be used as the unique weapon to answer a series of unsolved science puzzles. And, inversely, if our natural science frankly could ignore the mathematical rigor and deviate the necessary consistency premise, there would be neither natural science nor both the ‘order and accord’, which might just construct a logic negation of Einstein’s expectation.

       Therefore, either in the viewpoint of philosophy or a pure natural science investigation, the time consuming argument that ever took placed between Einstein himself and the main current science society in his era, which embraced the relative theory, is far from end. Some science philosophers pointed out: ‘parochial prejudices presented in different scholar departments, disputes caused by different schools of thought, unprofessional persons inviting ostracism from some special parties, etc., and, in a word, the forms of factional tendencies presented in science society always cause the resistance against any science discovery.’ Perhaps, all of these, still indispensably adding with another reality that any science research also belongs to a part of society actions of human, the current main science society does not wish to accept the exhort repeatedly supposed by the honest Einstein nearing to his end of life, some physical concepts might need some reflections every time period past, even being faced with such a strict challenge that the entire foundation of relative theory as well as all the modern physics ideal will possibly destroy for the discovering forms of superlight and sublight velocities. Confidently affirmed, no matter how human’s history develops in the future, it will never be possible to avoid such a task to how give a rational or logically agreeable answer to the Michelson-Morley experiment. Of course, after supposing the mission to make a global and historical rearrangement on the whole natural science system from the creation of Newtonian mechanics according to both the material-firstness and the logic-consistency principles, the writer cannot help being faced with a more serious problem that originally belongs to the region of pure sociology but natural science.

       Granted, it is the haste and earnest to seek unknown that made me unconsciously step into the area of fundamental research or purely fundamental research of natural science. Accordingly with the deepening cognition on natural science, the cognition about some sociological phenomena presented in science researches is also deepened too. Both the history and present seem to tell us such a reality: A series of difficulties do not really origin from the inner of science research but the outside, the insanity of a normal argumentation mechanism. Though it usually makes my heart be full of desolation and perplexity for me to encounter with kinds of unexpectedness over this time period, it is fortunate for the world to be progressing after all. If comparing with the fortune met by a lot of criticizers presented in history, the writer would be rather providential. In fact, if lacking of the determinative and seldom valuable support from the leaders of the university where the writer works, the encouragement originated from a lot of kind and ingenuous grand old men, craft brothers in the academia, and even the inspirit and brace from a lot of friends who are enthusiastic in national science but have never met each other before, the study would not be continued up till now. Of course, to these honest and effective supports and even some pressure caused by such a support, would the writer express sincere thanks and deep regret from the bottom of my heart.

       Science belongs to the whole human. However, no need for reticence, west scholars have devoted much more huge and historical contribution on the building of modern natural science system than east persons. Perhaps, just for it, it likes the real feeling easier produced by east intellectual that, under some refined and courteous appearances, a few west scholars usually involuntarily express some superiority complex, which might better be called as a kind of ‘excess self-belief’ or ‘thinking predominance’, though it is far from difficulty to be understood and can also possess a real existence foundation. A lot of scholars involving Einstein ever criticized east persons for the insufficiencies in ‘formal logic’ but, comparatively speaking, being relatively skilled in ‘dialectical logic’. However, when comparing with the serious criticism on the ‘excess metaphysics’ implicated in the relative theory, made by Mach, people should realize that, if ignoring the existence of a contradictory premises and disregarding mathematical rigor, any metaphysical expression not only becomes as an improper over-simplification of formal logic but also has constructed a fatal negation on formal logic that must take logic consistency as its complete connotation. Actually, it just is the too metaphysical over-simplification that makes the whole modern natural science system will impossibly disengage from a series of logic paradoxes, such as inertial system based upon a circle logic.

       Therefore, even though people not consciously consider if the valuation about east science thinking is right or not, while the main current science society, just for a series of important and primary puzzles to have not been solved, compelled to frankly or obscurely announce to abandon the ‘rationality principle – involving logical consistency’ while openly refusing any solemn and principal criticisms, all the science world would know: it will become a new contribution to the human knowledge offered together by east and west nations that the science research should be added with ‘a global consciousness (dialectical relationship and unity of conflicts)’ and ‘some meticulous thinking customs’ possessed by east nations.

       For a historical reason known well to all, there is almost not any mark imprinted by Chinese in the systematic investigation and building of modern natural science system. Up till now, the investigation in basic science made by Chinese and even the Chinese scholars abroad can only be classified into the religion of ‘tailing investigation’ in general. To the Chinese nation who ever possesses the bright old civilization, it is no more than a kind of dishonor. And, just for changing history, every Chinese descent not only should envisage the reality of such an existence but also need to sufficiently guard and thoroughly eradicate the ‘inaction consciousness’ belonging to the people living in colony or semi-colony, which is also originated from the historical reason and hides in the deep bottom of heart of every Chinese. While the natural science system being with a lot of unsolved puzzles over centuries, the ‘consciously or unconsciously excess romance on Nobel Prize’ is no significant except injuring the self-confidence indispensable to every self-respected nation. Affirmed, there is no authority before a series of world puzzles over centuries. Then, in order to build an independent natural science investigation system of china, it is of primary significance to explode blind worship, to erect the self-confidence necessary to the real natural science research and to advocate the science criticisms using strict science language. And, just for it, Chinese nation will win the reputation from the whole world while Chinese natural science research will really step into the process for world science development and self-support in the independent researching groups.

       Being really scientific, it must be natural and easy for people to accept. In natural science investigation, any arguments using strict science language are permissible and feasibly encouraged between different opinions. Believed, it is the inner nut for the science to possibly exist as well as the unique way for science to develop so rationally that to not degenerate into a new simple religion. Science belongs to the entire human, the human living in all the historical progress. In the ‘critic-successive and succeed-critical’ developing process of natural science, the reveal of the forms of material existences and material movements will always be of ultimate significance and, consequently, determine the cognition level of the era. In such a meaning, it might be said: both the appearance of Einstein and the reflection on Einstein in the human history would be natural. Believed, the different consciousnesses and the arguments are also possibly regarded as some necessary of history. Also in such a meaning, if comparing with the developing process of human cognition, any awareness formed in a single person would be too slight to be mentioned or, more exactly speaking, as a necessity. Also believed, compared with directly stating some particular conclusions, to openly demonstrate of the insufficiencies really existing in the deepening cognition would be more important. So, it is needed for people to call up the scientific criticism inspirit, upon which science should rely for living, while the writer wish to be a target in the science criticism and then offer a tiny but sincere contribution.

Yang Benluo

ShangHai JiaoTong University

Initially wrote in spring, 2001

Finished in January, 2003

       物质世界是一个彼此关联着的整体。对于本质上作为大数粒子集合的宏观物质世界，当其中某一个为人们关注的部分，在特定的条件下能够维持宏观表象不变的时候，人们总可以相信：那个真实存在的宏观表象一定对应于宏观差异最小的状态；同时，一个为人们关注的部分，在特定条件下进行着宏观意义的运动时，人们则可以期待：该宏观物质集合必然以一种最有效的形式自发地实现属于自身的运动。

      对于宏观物质世界的这样一种理性判断，相合于自然科学中一切变分原理的本质内核，也是人们可能为整个宏观力学构造一个基本可靠的变分原理的基础。仅仅于此，人们才能够对以出现宏观表象间断为基本特征的复杂变形，以及同样以存在宏观表象某种性质不连续现象为基本特征的复杂流动现象，即人们所说的“湍流”做出彼此逻辑相容、大概真实和合理的描述。

       任何一个形式表述系统都仅仅是条件存在，然而必需保持形式逻辑上的完备性和自洽性。因此，当人们应用无歧意的形式语言表现物质世界中不同理想化部分所呈现的不同规律的时候，那个被描述物质对象始终是第一位的。一切宏观物质总是粒子的，宏观物质的粒子本质与借助于微分方程所表现的连续宏观表象之间所存在的根本矛盾制约着整个宏观力学，同时，这种矛盾也自然地成为表现湍流这样一种复杂运动的本质困难。

符 号 表

拉丁字母符号

    表面积

*         流体粒子之间的平均距离

       流体的声速

*     加速度

       一般矢性函数

     物质集合M的初始构型

*         物质集合M在任意时刻所占剧的子空间

     一般矢性函数

   　物质元的初始构形

   　物质元在任意时刻所占据的子空间

  物质元在某时刻所占据的子空间

　　　一般矢性函数

　　　定容热容量

  泛指常数

      n阶连续函数 

      变形率张量或应变率张量

*          三阶Eddington旋转张量

*          总内能

      标量Poissin方程基本解

       单位内能

   与坐标轴对应的基矢量

　　　绕流物体的总表面力

　　　绕流物体的表面力的切向分量的“总和”

     函数记号

　　　　流动阻力，为在运动方向的分量

泛指某一物理量宏观表象

*        单位质量力

       涡块的总外力

     第个物理量的分布函数

    摩擦力

  摩擦力折算到单位体积上的净作用效果

    某体积元承受的质量力

     某体积元承受的折算到单位体积上净表面力

　　　单位体积物质承受的质量力

      单位体积物质承受的力(包括表面力的净效果)

　　　一般矢性函数

        二阶单位张量(恒等张量)

         体积元中的第个粒子的编号

          某组物理量(或独立方程)的编号

*        　 惯性张量

          涡块的总外力矩

           涡块的动量矩

         流场的特征尺度

        编号为的流线所占的空间位置

      Lame系数

       客观物质集合

       具有可跟踪性的物质元

       粒子模型的物质元

    物质元的质量

　　    第个粒子的质量

        与空间点X对应的客观物质元

        三维流形

          体积元中的粒子数

某组物理量(或独立方程)的总数

*              单位表面外法线方向

          泛指某组物理量

*              热力学压力

                  宏观物理量的强度量

点处物质元的第个物理量

点处在T时刻的第个物理量

      第个粒子对宏观物理量的贡献

       第个真实粒子的标记

  (11.3.9)

*           热流密度矢量

       升力

       三维Enclid空间

*          六维Enclid空间

       雷诺数

*           空间两点的位置向量

*         热力学状态参数熵

几何空间

     可为粒子—统计模型描述的流动区域

     与第I 个涡对应的子空间

       滑移速度（8.4.1）, (8.4.2c)

　　（§５.1.2）

　　　热力学温度

　　　在边界上的应力分量

　　　　实验测得的边界上的表面力分布

      边界上的应力向量的法向分量

     边界上的应力向量的切向分量

*           任意时刻

      参考时刻

      (1.4.2a)

       速度向量

      在处的速度向量

      第个粒子的速度

*        用实验方法测得速度值

   (5.3.4)似应改为

*          有限大空间域

      物质空间

点的物质元对应的有限体积

    存在涡现象的局部域

          “有序”的局部域  (7.4.5a)

       “无序”  的局部域  (7.5.2b)

   “充分紊乱（无序）”  的局部域  (7.4.6b)

        离散粒子速度分布的”解析延拓”

        离散粒子的真实速度分布

        流线上流体粒子的真实速度

　　　　表面力的功率耗散函数

　　　　  边界积分方程中的权系数

           损耗总功率(5.1.8),(7.6.1)

       体摩擦功率损耗

       面摩擦功率损耗

　　离散粒子对宏观意义上的整体运动速度的偏离

      子集合(刚体)的旋转角速度

    空间点的位置(Euler坐标)

       流体的物质坐标(Lagrange坐标)

      某一个确定的物质元标记(Euler描述)

 

希腊字母符号

 

     (§5.1.2),(5.4.3b)

固壁上的滑移摩擦系数

*         速度环量

      变化量

         Dirac函数

数性小量

      矢性小量

     Kronecker算符

      三阶Eddington张量

      散度

   流体表观动力粘性系数

    严格层流时,流体之间的摩擦系数

　　　 流体表观运动粘性系数

     严格层流时,与相应的运动粘性系数

  建立在流线或流面上的局部坐标系

      二阶应力张量

       流体分布密度

*          摩擦应力张量

      动量输运张量

       特征时间

       流函数（矢量势）

*          物质元的独立旋转角速度分布

　　　　 旋度（涡量）

       流体的旋度（涡量）

 

下角标

    表示流场入口处的有关参数

     表示流场边界的有关参数

    有关矢量（张量）的法向分量

     有关矢量在固壁处的切向分量

     有关物理量的参考值（相对于时间或空间）

*         通过实验测得的相应物理量

       涡块的质心参数

       某一物理量的临界值

   与涡有关的物理量

    上角标    

   矩阵或张量的逆

    矩阵转置

ノ    物理量的脉动值

顶标

-                  物理量的时均值

某体积域的余集

    时间变化率

    物理坐标的时间变化率

数学运算符号

•       点积算子

∶      二次点积算子

      叉积算子

      哈密顿算子，或称空间梯度算子

      物质梯度算子

     物理量的物质导数算子，或称随体导数算子,有时也记为

      小量

*      全微分算子

      偏微分算子

     线积分

     封闭曲面积分

     体积分

    求和

     极限

     一阶小量（与１比较）

        属于

        不属于

       不包括于

       任意的

       右包含左

       左包含右

        存在

       交

       和

      范数

     行列式

      正比于

      相邻性标记

      不相邻的标记

      定义相等

       恒等，有时也表示定义相等

        集合

    在条件下，从左边可得到右边 

湍流和理论流体力学理性重构

宏观力学基础分析（卷Ⅰ）

目录

0 前言

1 宏观物质模型和物质元

— 流体和变形体的形式定义和基本特征

1.1宏观物质微元的力学意义

1.2连续介质模型

1.2.1 连续介质的形式定义

1.2.2 连续介质微元

1.3 粒子统计模型

1.3.1 大数粒子系统的宏观描述

1.3.2 宏观物质宏观表象的空间描述和和假想物质元

1.4 变形和流动

1.4.1 宏观物质的可跟踪性

1.4.2 变形和流动的本质差异

2 Navier-Stokes方程和广义层流

— 流体力学的第一类动力学方程及其应用条件

2.1 严格分层流的基本形式特征

2.2 Newton摩擦应力机制的真实性及其物理内涵

2.2.1 Newton摩擦应力形式表述的构造

2.2.2 Newton摩擦应力机制的存在条件

2.3 物质导数

2.4 层流和Navier-Stokes方程

2.5 严格分层流

2.6 层流概念的延拓和经典Navier-Stokes流

2.6.1 层流概念的延拓和广义层流的提出

2.6.2 Navier-Stokes方程和“纯粹粒子”意义的流动

2.7 极慢Stokes流和Poiseulli流

3 涡与Euler流

— 流场的局部有序结构、流体力学第二类动力学方程与相关现象分析

3.1 涡的本质

3.2 涡的形式定义

3.3 粒子系统的有序结构和无序粒子系统中的无规运动

3.3.1 宏观物质的有序结构和变形

3.3.2 宏观物质粒子的无规运动

3.4 Euler流动和Euler方程

3.5 涡与“旋转运动”

3.6 Rukefusiji升力公式和Holmholtz涡量定理

3.6.1 Rukefusiji升力公式的物质基础

3.6.2 Holmholtz涡量定理的物质基础

4 无规运动和流体力学的一般动力学方程

  — 流动中流体的动量输运机制和湍流模式理论的物理基础

4.1 流体力学动力学基本方程的重新构造

4.1.1 流体粒子的宏观动量输运机制和动量方程的构造

4.1.2 动量输运机制物理内涵的补充分析

4.1.3 关于“动量原理”的一般性补充分析

4.2 动力学方程的几种特例

4.2.1 宏观物质运动中的有序结构和Euler方程

4.2.2 “层流”和赋予确定物质内涵的Navier-Stokes方程

4.2.3 “均混流”和通常意义上的Navier-Stokes方程

4.3 流体力学一般性动力学方程与Reynolds湍流方程

4.3.1 经典Reynolds方程的导出

4.3.2 Reynolds湍流方程存在问题的基本分析

4.3.2.1 Navier-Stokes方程的“真实性”问题

4.3.2.2 层流和湍流的物质基础问题

4.3.2.3 形式逻辑倒置的问题

4.4 流体力学动力学方程的形式特征分析

4.4.1 方程的恒不封闭性

4.4.2 “表观粘性应力”和宏观速度场泛函

4.4.3 流体运动复杂性的两种不同本质内涵

5 边界条件的不同形式表述及相应物理内涵

— 流体力学的运动学和动力学边界条件分析（上）

5.1 力的连续性和动力学边界条件的普适意义

5.1.1 动力学边界条件的提出

5.1.2 动力学边界条件的普适性及补充条件的构造

5.2 关于压力场的补充分析和边界条件的修正

5.3 广义层流运动以及粘附性边界条件的真实存在

5.4 Poiseuille流动实验的重新分析与“滑移边界条件”

5.5 关于不同边界条件的一般陈述

6 绕流最佳型线的界定及其应用分析

— 流体力学的运动学和动力学边界条件分析（下）

6.1 绕流最佳型线问题的提出

6.2 绕流最佳型线的形式定义

6.2.1 关于“流动阻力”的习惯认识

6.2.2 “绕流最佳化”的重新认定

6.3 绕流最佳型线的求解

6.3.1 基本数学模型

6.3.2 基本逻辑前提

6.3.3 经验系数的确定

6.4 不可压缩流绕流最佳型线的涡计算方法

6.4.1 不可压缩流研究中的不同基本问题

6.4.1.1 液体压力场求解的失真

6.4.1.2 气体动力学中不可压缩流假设物理基础的重新提出

6.4.2 流函数逼近方法

6.4.2.1 流函数逼近方法的基本思想

6.4.2.2 关于求解双旋度Poisson方程及定解条件的若干补充说明

6.4.3 边界积分方程 － 差分交叉逼近方法

6.5 关于构造完整计算模型的大概分析

6.5.1 一般分析

6.5.2 不可压缩流流场压力分布预测

6.5.3 液体和气体不可压缩性不同物理内涵的一般性分析

7 湍流的本质

— 存在局部变形的复杂流动

7.1 流动和变形

7.1.0 关于宏观物质运动的经典论述

7.1.1 纯粹变形和流动的形式定义

7.1.2 Lagrange空间和物质描述的逻辑前提

7.1.3 可跟踪性和流体的简单运动

7.1.4 简单流动中的Newton摩擦应力和Navier-Stokes方程

7.1.5 运动中流体的局部有序化自发倾向

7.2 液体和气体的简单流动

7.2.1 液体的简单流动

7.2.2 气体的简单流动

7.3 宏观表象间断面和“涡”

7.3.1 宏观表象间断面

7.3.2 涡

7.3.2.1 涡的物理本质

7.3.2.2 涡的形式表述

7.3.2.3 涡的“动力学方程”

7.3.2.4 关于“涡块”和“流块”

7.4 运动中流体的两种运动趋势和流场中的不同流动结构

7.4.1 运动中流体的两种不同趋势

7.4.2 流体运动结构的演化

7.4.2.1 缓慢流动

7.4.2.2 较快流动和流动结构变换中的一般性特征

7.4.2.3 较快流动的数学描述

    7.4.2.4 局部各向异性和一般湍流模型

7.4.2.5 Helmholtz分解和Ω-ε湍流模型的物理基础

7.4.2.6 流场中的“宏观结构”

7.5 湍流与流动形式的转捩

7.5.1湍流与层流以及湍流分类

7.5.1.1 简单湍流

7.5.1.2 “拟各向同性”湍流

7.5.1.3 流场结构

7.5.2 湍流转捩和稳定性分析

7.6 湍流的“可认识性”与“无规律性”的辩证统一

7.6.1 湍流的可认识性

7.6.2 湍流的“无规律性”

8 流体力学变分原理和复杂流动三区模型

   — 表现复杂流动现象的一般性简单模型

8.1 对于流体运动一般特征和若干基本概念的重新认识

8.1.1 宏观物质的粒子本质和流体运动规律的统计特征

8.1.2 流体微元的不可跟踪性和物质导数的有限真实性

8.1.3 摩擦应力动量输运机制的自均匀化本质与有限能力

8.2 物质运动的有效性原则和流体运动中的局部有序结构

8.2.1“极慢分子流”和流体运动中的“分块结构”

8.2.2 “流块”的基本物理特征和数学描述以及对于Euler方程真实性的重新理解

8.3 具有不同结构流场中的若干基本事实和基本假设的认定

8.3.1 流场是一个充满“宏观物质”的空间场

8.3.2 空间表述是流场宏观表象的唯一表述形式

8.3.3 宏观表象的可间断性和物质作用的连续性以及动力学边界条件的提出

8.3.4 流场的宏观表象在时间域上的连续性

8.3.5 流场满足大自然的有效性普遍原则

8.4 最小功率耗损原理

        — 属于整个大自然的一种基本变分原理和流体力学公理化演绎体系的一般表述

8.4.1 最小功率耗损原理的提出

8.4.2 一般流体力学公理化演绎体系的建立

8.5 存在足够大“局部有序流动结构 ― 涡”的一般流场与三区流动模型

8.5.1 三区流动模型的提出

8.5.2 不同子域中的不同流动规律描述

8.5.3 不同子域边界条件的确定

8.5.4 耗散函数和相应变分问题的提出

8.6 若干相关问题的重新思考

8.6.1 Prandtl边界层

8.6.2 Reynolds数

8.6.3 动力学发展过程的大概分析

8.7 两种实际流动状况的大概分析

8.7.1 管内流

8.7.2 圆柱绕流

9 流体运动分类及相关形式表述的逻辑关联

 9.1 涡和湍流的物理本质

 9.2流体运动分类和不同动力学方程的相互关联

 9.3若干补充说明

10 经典流体力学中压力场定义中的逻辑歧义及其辨析

10.1 经典理论中压力的基本定义

10.2 宏观物质的粒子本质和表面力的形式构造

10.3 液体和气体的本质差异以及应力的不同基本特征

10.3.1 固体、液体和气体的本质差异

10.3.2 运动中气体表观应力的物理内涵

10.3.3 运动中液体表观应力的物理内涵

10.4 “压力场”经验数据系统的重新构建

10.5 “一般动力学方程”中的逻辑不当

11 “物质第一性”和“逻辑自洽性”两个基本原则的辩证统一

11.1 宏观物质的粒子本质和宏观表象的构造

11.2 流体的“粒子本质”和“一般动力学方程”的构造

11.3 Navier-Stokes方程的重新诠释

       11.3.1狭义Navier-Stokes方程和广义层流（严格粒子流）

       11.3.2广义Navier-Stokes方程和“均混流”

11.4 涡（Vortex）和Euler方程

11.5 坚持自然科学研究中“物质第一性”和“逻辑自洽性”两个基本原则

附录

       (Turbulent flow, physical connotation of apparent stress and general dynamic equation of fluid dynamics - Momentum transfer mechanism of stress and physical foundation of turbulence models)

Contents

0 Preface

1 Model of macroscopic material and material element

¾ The formal definition and fundamental characters of fluid and deformation body

1.0 Introduction

1.1 Physical connotation of macroscopic material element

1.2 Continuous medium model

1.2.1 Formal definition of continuous medium

1.2.2 Continuous medium element

1.3 Statistical model of particle system

1.3.1 Macro description of a system with a large number of particles

1.3.2 Space specification of macroscopic representation and imagined material element

1.4 Deformation and flow

1.4.1 Traceability of macroscopic material

1.4.2 Essential difference between deformation and flow

2 Navier-Stokes equation and general laminar flow

¾-The first kind of dynamic equation and related qualifications

2.0 Introduction

2.1 Strictly laminated flow and principal characters

2.2 Reality and physical connotation of Newton friction stress mechanism

2.2.1 Construction of formal expression on Newton stress

2.2.2 Qualifications of Newton friction stress

2.3 Material derivative

2.4 Laminar and Navier-Stokes equation

2.5 Strictly laminated flow

2.6 Extension of concept about laminar flow and classical Navier-Stokes flow

2.6.1 Extension of concept about laminar flow and proposal of general laminar flow

2.6.2 Navier-Stokes equation and flow in pure particle significance

2.7 Extreme-slow flow and Poiseulli flow

3 Vortex and Euler flow

¾ The local-ordered structure of fluid field, the second dynamic equation of fluid dynamics and analyses on related phenomena

3.0 Introduction

3.1 Essentials of vortex

3.2 The Formal definition of vortex

3.3 The ordered structure of particle system and the misruled movement of disordered particle system

3.3.1 The ordered structure of macroscopic material and deformation

3.3.2 The misruled movement of particles of macroscopic material

3.4 Euler flow and Euler equation

3.5 Vortex and ‘rotation’

3.6 Rukefusiji lifting theorem and Holmholtz vorticity theorem

3.6.1 The material foundation of Rukefusiji lifting formula

3.6.2 The material foundation of Holmholtz vorticity theorem

4 Misruled flow and general dynamic equation of fluid dynamics

  ¾ The momentum transfer mechanics and physical foundation of turbulence models

4.0 Introduction

4.1 The reconstruction of the fundamental equation of fluid dynamics

4.1.1 The macroscopic-momentum transport mechanism of fluid particles and the construction of momentum equation

4.1.2 The physical connotation of momentum transport

4.1.3 The comment on university of momentum principle

4.2 The particular cases of dynamic equation

4.2.1 The ordered structure of moving macroscopic material and Euler equation

4.2.2 ‘Laminar flow’ and Navier-Stokes equation endowed with positive material connotation

4.2.3 ‘Homogeneous-mixed flow’ and a generally used Navier-Stokes equation

4.3 The general dynamic equation of fluid dynamics and Reynolds turbulence equation

4.3.1 The reduction of classical Reynolds equation

4.3.2 Elemental analyses on improprieties implicated in Reynolds equation

4.3.2.1 Enquiry on reality of Navier-Stokes equation

4.3.2.2 The material foundations of laminar and turbulent flows

4.3.2.3 The logic-reverse in Reynolds equation

4.4 The formal characters of dynamic equation of fluid dynamics

4.4.1 Eternal non-closure

4.4.2 ‘Representative viscous stress’ and the function of velocity field

4.4.3 The two distinct essentials of complexity presented in flow

5 Different formal expressions on boundary conditions and related physical connotations

¾ Analyses on kinematic and dynamitic boundary conditions of fluid dynamics (first half)

5.0 Introduction

5.1 The continuity of force and the universal significance of dynamic boundary condition

5.1.1 The proposal of dynamic boundary condition

5.1.2 The universality of dynamic boundary condition and added conditions

5.2 Comment on pressure field and the modification of boundary conditions

5.3 General laminar flow and the reality of adherence boundary condition

5.4 The reexamination of Poiseuille flow and ‘slipping boundary condition’

5.5 General statement on different boundary conditions

6 Definition on optimal outline of a streaming body and its usage

¾ Analyses on kinematic and dynamitic boundary conditions of fluid dynamics (second half)

6.0 Introduction

6.1 The optimal profile of streaming body

6.2 The formal definition of optimal profile of streaming body

6.2.1 Customary conviction on flowing resistance

6.2.2 Recognition on streaming optimization

6.3 The solution of optimal profile

6.3.1 Mathematical model

6.3.2 Logic premise

6.3.3 Determination of empirical coefficients

6.4 Vorticity-method for calculating optimal profile of incompressible streaming

6.4.1 Different problems presented in incompressible flow

6.4.1.1 The distortion of liquid pressure field

6.4.1.2 Re-proposition on the physical foundation of incompressible fluid presented in gas dynamics

6.4.2 Current function approach method

6.4.2.1 Fundamental thinking

6.4.2.2 Comments about the solution of Poisson’s bispinor equation and definition conditions

6.4.3 Boundary-integral equation – difference mixed-approach method

6.5 The construction of a complete calculation model

6.5.1 General analysis

6.5.2 Prediction on pressure distribution of incompressible fluid

6.5.3 Distinct physical connotations of incompressibility presented in liquid and gas

7 The essential of turbulence

¾ Complex flow with local deformation

7.0 Introduction

7.1 Flow and deformation

7.1.0 Classical statements about macroscopic movement

7.1.1 Formal definition on pure deformation and flow

7.1.2 The logic premise of Lagrangian space and material description

7.1.3 Traceability and simple flow

7.1.4 Newton friction stress and Navier-Stokes equation in simple flow

7.1.5 The spontaneous tendency of local-organization presented in flowing fluid

7.2 The simple flow of liquid and gas

7.2.1 Simple liquid flow

7.2.2 Simple gas flow

7.3 The interruption of macroscopic representations and vortex

7.3.1 The interruption of macroscopic representations

7.3.2 Vortex

7.3.2.1 The physical essential of vortex

7.3.2.2 The formal expression of vortex

7.3.2.3 Dynamic equation about vortex

7.3.2.4 ‘Vortex block’ and ‘flowing block’

7.4 Opposite kinematic tendencies presented in flowing fluid and different flowing structures

7.4.1 The two opposite kinematic tendencies of flowing fluid

7.4.2 The evolution of flowing structures

7.4.2.1 Slow-flow

7.4.2.2 Rapid-flow and general characters presented in the evolution of flowing structures

7.4.2.3 Mathematical description on rapid-flow

    7.4.2.4 Local anisotropic character and general turbulence models

7.4.2.5 Helmholtz decomposition and the physical foundation of W-e turbulence model

7.4.2.6 The ‘macroscopic structure’ of fluid field

7.5 Turbulence and transition of flowing structure

7.5.1Turbulence, laminar flow and classification of turbulence

7.5.1.1 Simple turbulence

7.5.1.2 ‘Pseudo-isotropic’ turbulence

7.5.1.3 Structure of fluid field

7.5.2 Turbulence transition and stability analysis

7.6 Dialectical unity between ‘intelligibility’ and ‘irregularity’ of turbulence

7.6.1 Intelligibility of turbulence

7.6.2 Irregularity of turbulence

8 Variational principle of fluid dynamics and three-region model of complex flow

¾ Generally simple model to express complex flow phenomena

8.0 Introduction

8.1 Recognition on the general characters of fluid movement and some fundamental concepts

8.1.1 The particle essential of macroscopic material and the statistical character of fluid flow

8.1.2 The untraceability of fluid element and the finite reality of material derivation

8.1.3 Self-homogenization essential and the finite capability of momentum transport mechanism of viscous stress

8.2 The effective principle of material movement and local-ordered structures presented in fluid flow

8.2.1 ‘Extreme-slow flow’ and the ‘block-structure’ of fluid flow

8.2.2 Physical character and the mathematical description of ‘flowing-block’ and recognition on the reality of Euler equation

8.3 Basic specifics presented in a fluid field with different flowing structures and related fundamental presuppositions

8.3.1 Fluid field as a space field full of macroscopic material

8.3.2 Space description as the uniquely universal specification on macroscopic representation presented in fluid field

8.3.3 The permissible interruptibility of macroscopic representation, the indispensable continuity of material reactions and the supposal of dynamical boundary condition

8.3.4 The continuity of macroscopic representation in time domain

8.3.5 Fluid field satisfying with the universal effectiveness principle of nature

8.4 Least power-dissipation principle

        ¾ Universal variational principle belonging to the nature and the general expression of an axiomatic system of fluid dynamics

8.4.1 The supposal of least power-dissipation principle

8.4.2 The building of a general axiomatically deductive system of fluid dynamics

8.5 Vortex ¾ local-ordered structure with an enough breadth and the three-region model of general fluid field

8.5.1 The supposition of three-region flowing model

8.5.2 Different flowing laws presented in different sub-domains

8.5.3 Connecting conditions between different sub-domains

8.5.4 Dissipation function and a related variational problem

8.6 Reconsideration on a series of problems

8.6.1 Prandtl boundary layer

8.6.2 Reynolds number

8.6.3 Dynamic evolution

8.7 General analysis on two actual flows

8.7.1 Inner flow in a pipe

8.7.2 Streaming around a cylinder

9 Classification of fluid flow and logical connection between related formal expressions

 9.0 Introduction

 9.1The physical essential of vortex and turbulence

 9.2 The classification of fluid flow and the relationship of different dynamic equations

 9.3 Added comments

10 The logical ambiguity of pressure field presented in classical fluid dynamics and its re-discrimination

10.0 Introduction

10.1. The basic definition of pressure in classical theory

10.2. The particle essential of macroscopic material and the formal construction of surface force

10.3. Intrinsic difference between liquid and gas as well as the different characters of stress

10.3.1 Solid, liquid, gas and their intrinsic differences

10.3.2 The physical connotation of representative stress of flowing gas

10.3.3 The physical connotation of the representative stress of flowing liquid

10.4. The reconstruction of empirical data library about pressure field

10.5. Logic improprieties presented in ‘general dynamic equation’

11 Dialectical unity between ‘material-primary’ and ‘logic-consistency’

11.0 Introduction

11.1 The Particle essential of macroscopic material and the construction of macroscopic representation

11.2 The particle essential of fluid and general dynamic equation

11.3 Reinterpretation on Navier-Stokes equation

       11.3.1 Special Navier-Stokes equation and ‘general laminar flow (strict particle flow)’

       11.3.2 General Navier-Stokes equation and ‘homogeneous-mixed flow’

11.4 Vortex and Euler equation

11.5 Persevere both the fundamental principles of natural science – ‘material primary’ and ‘logic-consistency’

 

Appendix

Turbulent flow, physical connotation of apparent stress and general dynamic equation of fluid dynamics - Momentum transfer mechanism of stress and physical foundation of turbulence models

0. Introduction

1. The rebuilding of fundamental dynamic equations

1.1 The particle essential of fluid and the macroscopic representation of flowing fluid

1.1.1 The establishment of macroscopic physical quantities

1.1.2 The misruled motion of particle

A.1 Added comment on difference between disorder and misrule

1.2 The momentum conservation of particle system and the variation of macroscopic momentum

1.3 General dynamic equation

1.4 Pressure presented in fluid field

1.5 Apparent viscous stress

1.6 Compatibility between particle momentum conservation and macroscopic dissipation

A.3 Added comment on the incompatible expressions of stress presented in statistical mechanics

2. The special inferences of general dynamic equation

2.1 Local self-organization and Euler equation

A.4 Added comment on Lagrangian specification

2.2 Laminar flow and a special Navier-Stokes equation with certain material significance

2.2.1 Strictly laminar flow

2.2.2 Newton viscous theorem and generally laminar flow

2.2.3 Independent Newton viscosity and special Navier-Stokes equation

A.5 Added comment on initial Navier-Stokes equation

2.3 Homogenous-mixed flow and general Navier-Stokes equation

3. Reynolds turbulence equation

3.1 Classical inferring on Reynolds turbulence equation

3.2 Improprieties presented in Reynolds turbulence equation

3.2.1 The ‘reality’ of Navier-Stokes equation

3.2.2 The different material foundations of laminar and turbulence flow

3.2.3 Logic inverse

4. The formal characters of general dynamic equation and turbulence

4.1 The eternal incompleteness of general dynamic equation

4.2 Special and general Navier-Stokes equation

4.3 Apparent stress as the functional of velocity field and turbulence models

4.4 Anisotropy, inhomogeneity and brief interpretation on w-e model

4.5 The particle essential of turbulence and the two types of distinct complexities

4.5.1 The complex deformation of macroscopic material

4.5.2 Global complexity presented in flowing

5 Conclusion

前    言

       毋庸置疑，是Newton，Euler，Cauchy，Maxwell等许多科学巨匠将人类对大自然的认识带到了这样一种理性层次的认识阶段，使用以无矛盾为最基本内涵的数学语言表现着物质世界可能存在的不同抽象同一性。整个自然科学体系的开创者们在探索真理过程中所闪耀的智慧光芒将永远照耀着人类。

       但是，人类对于物质世界的理性认识总是逐次递进的和逐步严谨化的。无论从形式逻辑语言自身的完善程度，还是从人类对于物质世界的认识水平考虑，人类认识的进化必然地被赋予了时代的烙印。当Euler于18世纪30 年代将“连续介质(continuum media)”概念引入宏观力学，从而使得人类对宏观物质运动的形式化描述成为一种可能的时候，只是经历了一个半世纪，在19世纪的末叶才由德国数学家R. Dedekind对“连续统(continuum)”的抽象内涵首次作出了界定。从物理上考虑，连续介质无论怎样切割，仍然是连续介质而不能成为粒子，而粒子无论怎样拼凑也无法构成连续介质。

       在人类的认识史中，几乎每经历一段时间，特别是当人们意识到长时间地面临某种重大科学难题的困惑的时候，不得不重新反省那些曾经被确信了的认识。应该说，对于认识的重新认识与对认识中非理性的批判，不仅成为科学得以发展的必要前提，而且也真实地刻画了人类理性认识的承继性特征。

       原则上，现代自然科学体系应该是一个严密的、彼此关联着的整体。当人们通过若干人为构造的“概念”，将某一类理想化物质对象以及它们的运动与一个本质上不具任何物理内涵的形式系统构造一种具有确定意义的逻辑关联，并且依靠演绎逻辑对这样一类本质上并不真实存在的物质对象在不同特定条件下的运动做出预测的时候，概念自身与被描述物质对象之间所存在的严格对应具有根本的意义。更明确地讲，在任何一个特定的形式系统中，那个形式表述仅仅是人们对于物质对象所作理想化假设的逻辑必然。如果这种理想化假设基本符合物理真实，那么，这样一个形式表述系统成为一种大概可靠的描述。

       因此，人们针对被描述物质对象所作的理想化认定，而不是某一个仅仅条件存在的特定公式，对于使用无歧义形式语言的整个自然科学体系而言，具有前提性的意义。事实上，在一个形式系统的内部，即使所有的演绎推理不存在任何逻辑上的不自洽，人们可能得到的所有推论也仅仅是最初物理学陈述的重言式，本质上不包含任何新的内容。而人们通常所说的“自然规律”，无非是不同“理想化”物质对象在不同特定条件下所表现的“抽象同一性”而已。相反，一切能够满足某种特定理想化定义的物质对象，也必需满足这些形式表述的抽象同一性，否则，它就不成为那个已经被同一化界定了的理想化物质对象。任何形式表述的自然规律都仅仅本质地蕴含于同一化的理想化物质对象之中。可以说，正是在这样一个前提性的认识上，形形色色的经典理论出现了严重的认识倒置。

       纵观整个自然科学体系，除了对物质对象做出某种理想化假设，以消除相关现象中某些不太重要的部分，人们本质上不可能为大自然构造某种规律。甚至，那个可以被认为是普遍存在的“最有效法则”，或者理论物理学中的“最小作用原理”，仍然只是人们对那个“自存和自为”的大自然所作的一种符合理性的人为认定。

       自Reynolds完成他的著名的“湍流转捩”实验以后，人们重复地指出：湍流是“摆在人们面前的跨世纪的科学难题”；“虽然包括许多伟大学者在内的长达100多年的顽强努力，而其基本机理至今仍未弄清，这在整个自然科学史上也是不多见的”，[1] 从而成为对“理论和实验的挑战”。[2]

              既然，面对的是世纪性的重大科学难题时，人们不得不首先对宏观物质的“连续介质假设”这样一个最基本的逻辑前提的合理性进行认真反思。而且，考虑到创建经典宏观力学体系时的数学手段远未完备，对大自然的认识也远未像现在这样深刻，人们还不得不对“物质导数”定义、“Cauchy应力定理”以及“Navier-Stokes方程的逻辑前提以及相关的表现能力”等这样一系列宏观力学中的最基元概念重新进行严格的审视。当然，也正因为任何形式表述系统仅仅建立在某种理想化假设的物质对象之上，物质对象的真实运动与形式表述系统存在着永恒的差异，因此，人们不可能依赖对某一个形式系统进行不考虑逻辑前提的无穷延拓，对期望表现的所有物质真实做出有意义描述。在经典流体力学中，当人们断言Navier-Stokes方程体系的普适性以及必需成为解决湍流的唯一基础时，一个重大的困惑在于：在人们确信这种论断的时候，几乎从来没有认真研究这个形式表述得以存在的逻辑前提和属于这个理论体系的有限论域。当然，人们也几乎从来没有认真思索，限于那个时代的人们的认识能力，在构造这个基本方程的具体推导过程中可能存在的大量逻辑不自洽和物理概念紊乱的问题。

       建立在无歧意“形式语言”基础之上的自然科学体系，其全部存在基础仅仅在于一个相关形式表述与其描述的理想化物质对象之间的严格逻辑一致性，以及不同科学陈述之间的无矛盾性。即使人们确信某一个形式系统与其所描述的理想化物质对象之间形成严格的逻辑对应，人们同样没有理由相信，这个理论体系能够具有一种没有限制的预示作用。

       在《物理百科全书》中，人们曾经把“理论物理学”合理地称之为“数学语言写就的物理学”，以期望充分地表现这个特定学科必须具备的逻辑严谨性。[3] 但是，实际上，对于逻辑严谨性的漠视已经成为物理学研究中的一种普遍的真实存在。并且，本质上因为大量的前提性问题没有真正得到解决，以及严重违背演绎逻辑基本要素的“中间假设”几乎在物理学的许多论证中随处可见，对于“数学推导所必须的严谨性”表现为一种纯粹“人文性质”的随意取舍，似乎取得了一种完全“合法”的地位。正因为此，曾经对现代湍流理论进行了许多独立的研究，作为当代著名理论物理学家之一的Landau，在其对所著，对当今物理世界具有一定影响的《理论物理教程》的《非相对论量子力学》一卷的“序言”中，坦率地把理论物理中的数学严谨性称为“自欺欺人(Self-deception)”。[4]

       众所周知，数学严谨性的全部内涵仅仅在于无矛盾性。因此，在自然科学研究中，公然将对数学严谨性的忽视视为为一种可接受的普遍原则，应该极其可怕，也极其可悲。在这个意义上，人们可以说，20世纪后半叶在科学世界中涌现的“非理性主义（Irrationalism）思潮”并非偶然，它们不仅与人们通常所说的“宗教哲学”、“信仰主义”以及“存在主义”这样一些不同的哲学流派直接关联，更为本质地源于自然科学中大量存在逻辑不自洽现象的这样一种真实。[5]

       其实，对于认识中存在某种矛盾或者不自洽，并不可怕，甚至可以说是深化认识过程中的一种正常。可怕的是对于任何矛盾的掩饰，乃至粗暴地拒绝批判。在自然科学发展过程中，恰恰需要对于认识中任何存在的不自洽的揭示和批判，才可能达到深化人们认识的目的。

       在整个自然科学中，如何自觉地认识一切形式表述体系仅仅具备有限真实性，严格保持形式体系自身的逻辑严谨性，乃至保证形式体系与被描述理想化物质对象之间所必需具备的严格逻辑自洽性，以及有限真实性和逻辑严谨性之间的辩证关联都是一个大是大非问题。正因为任何形式表述体系仅仅建立在对于物质对象某种理想化假设的认定之上，所以，一切合理的形式表述系统仅仅具有有限真实性，而且，必然是条件存在的，相应存在一个确定的有限论域。另一方面，无论一个形式表述与物质真实之间存在多大的差距，但是，作为一个物理学陈述，以及这个陈述与特定的物质对象之间，必需保持严格意义的逻辑相容性。对于一个自身存在悖论的物理学陈述，没有任何意义。当然，人们可以相信，正是对逻辑严谨性的公然忽视，成为自然科学中许多重大难题长时间没有得到解决的根本原因。而且，当人们面临着愈益复杂的物质世界需要认识的时候，在公然容忍科学语言体系必需的无歧意准则遭受破坏的同时，自然科学存在着被重新推向神学的重大危险。

       经历一个多世纪几代人持续不断的努力，人们对于流体运动中呈现的种种复杂现象已经具备了相当充分的了解，同时得益于数学工具自身的完善以及对于物质世界自身认识的深刻化，这一切都为湍流疑难的最终解决已经提供了可能。但是，怎样才能够称得上“湍流疑难”得以最终解决的问题本身，本质上同样需要做出具有严格意义的科学界定。可以相信，湍流问题的最终解决绝非意味着再增加几个“湍流模型”，在已经难以计数的湍流模型中，仅仅增加若干个模型必然显得“过分平凡”了；同时，也并不意味着人们能够提供一个适用于湍流或者一切流动现象的普适的“数学模型”，这一思想恰恰违背了我们一再期望表现的基本哲学理念。所谓湍流疑难的最终解决，本质上应该包容以下几个主要方面的内容：

（1）       指出产生湍流的机制和湍流区别于人们所说的一般流动现象的本质内涵。等价地说：除了揭示流场之所以出现流动形式变化的物理机制以外，对蕴含于“层流（非湍流）”和“湍流”两种流动现象中“彼此相异”的“抽象同一性”，需要做出具有严格物理意义和形式意义上的界定。此处所谓的“抽象同一性”，就是蕴含于“同一类”现象中可以加以“形式定义”的共性。当然，一切湍流现象中共同存在的本质特征，对于“非湍流”不允许存在，反之亦然；

（2）       如果说“科学家的作用不应当是使工程师耻于使用一个有价值的工具，而应当或者确定它为什么行得通，或者向他提供一个更好的方法”，[1] 那么，需要为许多成功应用于湍流研究的半经验方法提供理论依据以及可能改进的途径；

（3）       指出相关描述的逻辑前提和限度。

澄清这些问题，对于在物理上揭示湍流的本质，以及在哲学上如何捍卫基本的理性原则其实都是必要的。否则，在从“将湍流界定为无规则流的同时而研究它的运动规律”的逻辑循环中得以解脱的同时，人们将陷入“企图完全真实地描述那个不可能完全真实描述的物质世界”的另一个循环逻辑之中。

       为了帮助读者对全书有一个总体意义上的了解，针对书中所讨论的内容做一个大概的分类，它们可以分为以下几个主要部分：

（1）       第1章题为“宏观物质模型和物质元”。相关讨论为宏观力学所描述的物质对象以及定义于其上的物理量首先做出明确的界定，它希望告诉人们这样一个明确的信息：一切形式表述本质上都是此处所作形式认定的逻辑必然，从而根本改变了经典理论中实际上将基本公式视之为某种“无条件存在”乃至“整个逻辑推理的全部基础”的严重反常；

（2）       从第2章到第4章是针对如何构造基本方程所作的讨论。与经典理论中的相关分析不同，不仅这些基本方程的基础都是针对“宏观物质对象”所作的“理想化形式认定”，而且，在不同方程的构造中，仍然遵循“演绎逻辑”必须严格遵循的“从一般到特殊”的基本法则。因此，在第2章中，那个依然“条件存在”的“一般性动力学方程”，成为进行一般流动分析的基础，并且，将取代在哲学理念和数学推理存在明显错误的Reynolds湍流方程，而第3章中出现的Navier-Stokes方程以及第4章中的Euler方程，仅仅是与某些特定条件对应的“约束映射”，作用于这个一般性方程而得到的不同“象”方程。并且，在此基础上，人们完成了对于“一般层流”以及“涡”的形式定义；

（3）       第5章和第6章是针对边界条件所作的讨论。相关讨论指出，重新给出的固壁上的“动力学边界条件”，本质上表现了“作用力和反作用力必须互等”这样一个不可缺省的“力”的“连续性”条件。至于经典理论中的“粘附性边界条件”，作为动力学边界条件的一个特例，仅仅存在于本质上是“粒子流”的“广义层流”之中。根据重新提出的动力学边界条件，人们可以为绕流体的耗散功率做出形式定义，从而为最佳型线的确定提供逻辑前提；

（4）       第7章名为“湍流的本质 — 存在局部变形的复杂流动”。该章对于“流动和变形”、“简单流动和复杂流动”、“涡的形式定义及产生机制”以及流场中出现的不同“流动结构”等一系列问题进行了总结性的分析。在第8章，再次提出了流场“三区模型”的问题，并且，根据普适的“最小作用原理”，为流场的一般性描述提供了一种范例。而在第9章，为流体运动的分类以及不同流动形式的逻辑关联构造一个“图”；

（5）       第10章，针对“经典流体力学中压力场定义中的逻辑歧义及其辨析”问题进行了分析。应该说，该章中对于“一般性动力学方程”中相关论述中存在的某些不足进行了纠正，重新指出经典流体力学中压力场定义中的逻辑歧义，进而较为合理地揭示了相同形式表述可能蕴含的不同物理内涵；

（6）       最后，提供了一个英文写成的附录：湍流、流体力学表观应力和一般性动力学方程的物理内涵 — 应力的动量输运机制与湍流的物理基础 (Turbulent flow, physical connotation of apparent stress and general dynamic equation of fluid dynamics - Momentum transfer mechanism of stress and physical foundation of turbulence models)。一般而言，该文属于第2章和第10章的一个综合。为什么不直接修正第2章相关论述中存在的某些不当，而采用这样一种迂回的方式，其目的仅仅在于：相对较为客观地揭示一个“认识深化着”的真实过程。

       总之，和经典理论相比，其最大分歧或者特点在于：作为全部推论基础的不再是某一个“无条件存在”的形式表述，而是针对那个特定的物质对象 — 粒子系统所作与事实基本一致的不同“理想化”认定。

       不能不再次声言，一个认识者个体在认识过程中总难免出现形形色色的局限性，其认识能力是十分有限的。对于认识的重新认识的过程，首先包括一个认识者个体对于自身认识过程的不断反省。特别对于我这样一个非专业的流体力学研究者，由于对目前湍流研究的现状缺乏详尽的了解，许多论述难免偏颇和失当，不洽乃至错误之处期盼人们指正。

杨本洛

2001年秋

前言参考文献

[1]  是勋刚，湍流，天津大学出版社，1994

[2]  胡非，湍流、间隙性与大气边界层，科学出版社，1995

[3]  S. P. Parker，物理百科全书，科学出版社，1990

[4]  L. D. Landau & E. M. Lifshitz, Quantum mechanics, Butterworth-Heinemann, 1997

[5]  Paul K. Feyerabend, 周昌忠译，反对方法，上海译文出版社，1992

[6]  杨本洛，经典热力学中若干基本概念的探讨，科学出版社，1996

[7]  杨本洛，流体运动经典分析，科学出版社，1996

[8]  杨本洛，理论流体力学的逻辑自洽化分析，上海交通大学出版社，1998

[9]  杨本洛，自然哲学基础分析 — “相对论”的哲学和数学反思，上海交通大学出版社，2001

Introduction

Beyond doubt, it is Newton, Euler, Cauchy, Maxwell and other great science master who guided the human cognition on nature into such rational level to use mathematical language, which takes non-contradiction as its total fundamental connotation, to express the abstract identity implicated in different idealized material objects. The intelligence brightness shone by these creators of the modern natural science system will always enlighten human.

       However, the rational cognition on material world always progresses and reaches the rigor step by step. From the viewpoint of either the self-completeness of formal logic language or the level of cognition on material world, any deepening of human cognition must be endowed with the time brand. After Euler initially introduce the concept of continuum media into macroscopic mechanics in 30 years of 18 century, it underwent one and half century that the abstract connotation of continuum was exactly exposed by German mathematician R. Dedekind in the end of 19 century. In physics, continuous medium will never become particles no matter how divided while particles will never be scrambled into a continuous medium no matter how many the particles are.

       In the human cognition history, almost every after a special time interval and, especially, while being confronted with some puzzles for a rather long time, people cannot but reflect on these judgments that have been seemingly convinced. It has to be said: the recognition on cognition and the criticism on every irrationality presented in classical cognition not only become a necessary premise for science to develop but also veritably depict the successive character of human rationality cognition.

       In principle, the modern natural science system should be a compact whole where its different parts rely upon each other. While people, by the aid of some artificial concepts, constructing a logic connection between a type of idealized material object as well as the idealized movement with a particular formal system that is not of any physical connotation in essential, and then according to a purely deductive logic and supplying a prediction on the possible motion made by these idealized material object that does not really exist, it must be rationally realized by us: it is of most essential significance for a strict logic correspondence to exist between the artificially supposed concepts and the idealized material objects. More exactly speaking, in a formal system, these particular formulas are only as the logic necessity of idealization on the described material object. If the idealization coincides with the basic physical reality, such a formal expression system will be generally reliable.

       Therefore, it is not an only qualifiedly existing formula but the idealized assumption on the described material object would be with the primary significance to the natural science system using an unambiguous formal language. In fact, restricted within the inner of a formal system, any inferences would be the tautology of the initial physical statement but without any extra connotation provided any logical inconsistency does not present. And, the order of nature, so called by us in general, is no more than the abstract identity existing-in-itself in the idealized material object. Inversely, any material object coinciding with such an idealization must content itself with the formally expressed abstract identity for, otherwise, it would not be the idealized material object. Any formally expressed natural law can only be logically implicated in the identically idealization on material object. Just in such a primary idea, it might be frankly said: in logic, the conventional cognition presented in almost every classical theory system has been severely inversed.

       Taking a panoramic view over the modern natural science system, expect making some idealization on the material object to eliminate some unimportant things presented in related phenomena, nothing can be done by us in essential. Even we consider the most effective principle that can be regarded as a universal statement, namely the least action principle in theoretical physics, the principle would still be as an artificial conviction on the ‘self-existing and self-acting’ material world, which can generally agree with the rationality expected by people.

       Since Reynolds empirically found the ‘turbulence transition’ in the century before last, people have repeatedly pointed out: Turbulence is as a trans-centuries science puzzle confronting before human; Up till now, the fundamental mechanics of turbulence has not been cleared though a lot of researchers involving many great scholars have made rather hard endeavor yet, which is seldom seen over the total natural science history; It has constructed a strict challenge to both the theory and experiment; etc..[2]

       Now that, faced with such a hard nut to crack, people cannot firstly reflect the rationality of assumption on continuous medium, which is the fundamental logic premise for all the classical analysis to possibly exist, and then make a strict reexamination on a series of elementary concepts, such as material derivative, Cauchy’s stress theorem, both the qualified condition and finite expression capability of Navier-Stokes equation. Don’t forget, during the different eras for our predecessors to create these classical theory systems, the mathematical tool was far from completeness while the cognition on the great nature far from deepness either. And, just for any formal system can only base on some idealization on material object and then be with some identical difference from the real movement made by the described material object, it is impossible for us to make an infinite extension from a single formula and construct a significant description on the reality we want to express, but to not mind both the logic premise and rigor. While people affirming Navier-Stokes equation to be as the unique foundation to research fluid flow and solve the turbulence puzzle, a huge baffle would lie in such a too abnormal fact: In the whole classical fluid dynamics, the logic premise and finite discourse universe of the fundamental equation have never been strictly studied and, consequently, it is impossible for us to imagine a lot of logic inconsistencies and confusions of physical concepts to present in this equation.

       To the natural science system using an unambiguous formal language, its total foundation would lie in the exact logic compatibility between a formal system and its idealized material object as well as the strict non-contradiction between different statements. Besides, even though strictly corresponding with the described material object in logic, still rationally believed, any formal system will not be of the capability of prediction without end.

       In ‘Encyclopedia of Physics’, people ever reasonably call theoretical physics as a physics written in mathematics in order to show the logic rigor particularly possessed by this subject.[3] But, actually, the unconcern or detachment about logic rigor universally exist in the physics investigation. And, essentially for a lot of elementary problems unsolved and the reality for forms of ‘middle-assumptions’ impermissible to deductive logic to be easy found everywhere, the voluntary acceptance or rejection of logic rigor necessary to any mathematical deduction seems to occupy a legal position, which can only be called as a purely humanism interpretation. As it is, in the preface of ‘Quantum mechanics (Non-relative theory)’, which is the third volume of the famous ‘Course of theoretical physics’, Landau frankly accounted ‘mathematical rigor in theoretical physics’ to be as ‘self-deception’. [4]

       Known well to everybody, the total connotation of mathematical rigor would be implicated in non-contradiction. Then, in the natural science researching, it is no more than rather fearful and also rather woeful for us to have no alternative but accept the disregarding of logic rigor to be as an acceptable universal principle. Then, in such significance, it might be said: the irrationalism trend of thought represented in the science world, in the later half of 20 century, would neither be by accident nor only rely upon a series of philosophical genres, religion philosophy, fideism or existentialism, said by people. A much realer and more fundamental foundation lies in the reality that a lot of inconsistencies really exist in our natural science system.

       In fact, the existence of some paradoxes or inconsistencies would not be worth to dread but, even more exactly speaking, be just as normality presented in the deepening cognition. The things for us to deeply dread would be the concealment of any contradiction and even the rough refusal to any criticism. In general, it is the revelation and criticism of any discord that make human cognition be possibly deepened.

       Basing upon the endeavor successively made by many generations over more than a century, people have enough information about kinds of complicated phenomena presented in fluid flowing and, benefited by the completeness of the mathematics self and the deepened cognition on material world, foresee the possibility to finally solve the turbulence puzzle. But, in the first, it is needed to make a rational definition about the proposition itself: what can be called as the solution of such a historical puzzle. Believed, the finial solution of turbulence puzzle never means either some turbulence models to be still added, which is too trivial while the innumerable models existing, or a universal and unqualified ‘mathematical formula’ that can be used to express every complicated flowing phenomenon, which opposes to the fundamental philosophical ideal we want to express again and again. In essential, the final solution of turbulence puzzle must consist with such a series of basic contents:

(1)    Point out the mechanism to create turbulence and show the essential connotation of turbulence differing from the common flowing phenomena generally said by people. Equivalently speaking, besides the physical mechanics to generate the variation of flowing forms, the distinct abstract identity respectively implicated in turbulence and non-turbulent flowing should be strictly defined in both the physical and formal meanings. And, the abstract identity said here is no more than the possibly formally defined common character of same class of phenomena. Consequently, all the essential characters exiting in turbulence can impermissibly present in any non-turbulent flowing and vice versa;

(2)    If we can rationally say that the effect of a scientist would not make engineer be ashamed to use a valuable tool but lie in making him know why the tool is permissible and even supplying him with a nicer method, it is needed for us to provide a reliable theoretical basis and some amelioration way for the semi-empirical methods to be successfully used in turbulence investigations;

(3)    Besides, supply a positive logic premise and a definite limit for the related expression.

       Clearing of all of these is necessary to reveal the turbulence flowing in physics as well as to guarantee the fundamental rational principle in philosophy. Inversely, just ridding of the circle logic constructed by studying the law of turbulence while turbulence being defined as disordered flowing at same time, we will be trapped into another circle logic wanting to absolutely really describe the material world to be impossibly abstractly described.

       Only for the convenience of global cognition on this book, the contents discussed would be classified into some main parts as following

(1)    The first chapter is named as ‘model of macroscopic material and material element’. The related discussion firstly makes a certain formal expression on the material object possibly described by macroscopic mechanics as well as the physical quantities defined in the material object and then want to show such positive information: every formal expression is only as the logic necessity of the idealized conviction on material object and then changes the strict anomaly that a particular formula has been regarded as an unqualified expression and even the total foundation to make all the inferences in the classical theory;

(2)    All the discussion presented from the second chapter until forth chapter aims for how to construct different fundamental equations. Differing from the related classical arguments, these fundamental equations unexpectedly base upon the convictions on the idealized material object and, besides, all of these follow the principle ‘from generality to particularity’ any deductive logic must strictly follow. Then, the general dynamic equation inferred in the second chapter becomes the foundation to infer other forms of dynamic equations, though which is still qualified, and should be used to replace the Reynolds turbulence equation with a series of evident improprieties in both philosophical ideal and mathematical deduction. An inexact-called Navier-Stokes equation and Euler equation respectively presented in third and forth chapters are nothing but the images of some constraint mappings acted on the general dynamic equation while the constraints correspond with different special conditions. And, accordingly, the positive definitions on ‘general laminar flow’ and ‘vortex’ can be formed;

(3)    The fifth and sixth chapters discuss boundary conditions. It is demonstrated: the dynamic boundary condition re-supposed essentially shows the continuity condition about ‘force’, which is indispensable to coincide the universal equivalent law of action and reaction. As for the adherent boundary condition presented in the classical theory, it may be regarded as a particular case of dynamic boundary condition and only presents in the ‘general laminar flow’, which equals with a pure particle flow in essential. Based upon the re-supposed dynamic boundary condition, the dissipative power of a streaming body can be logically defined and then supply a prerequisite to determine the optimal profile of a streaming body;

(4)    In the seventh chapter, named as ‘Essential of turbulence - Complex flow with local deformation’, a series of premise problems, such as ‘flow and deformation’, ‘simple and complex flowing’, ‘formation of vortex and its physical mechanism’ and ‘different flowing structures presented in fluid field’, are summarily discussed. In the eighth chapter, the problem about ‘three-region model of complex flow’ is brought forward again, which supplies a common example for the general analysis of fluid field based on the ‘least action principle’. And, the ninth chapter supplies a chart that shows the classification of fluid flow and logical connection between related formal expressions;

(5)    The tenth chapter discusses the logical ambiguity of pressure field presented in classical fluid dynamics and supplies a new re-discrimination. It should be said that some insufficiencies presented in the construction of general dynamic equation have been reclaimed. And, while some logical ambiguities presented in the classical definition on pressure field being pointed out, different possible physical connotations implicated in same formal expression would be revealed;

(6)    In final, an appendix named as ‘Turbulent flow, physical connotation of apparent stress and general dynamic equation of fluid dynamics - Momentum transfer mechanism of stress and physical foundation of turbulence models’ is added. In general, it is as a combination of the second and tenth chapters. The aim why for us to not directly revise these insufficiencies presented in the second chapter would lie in rather objectively showing a real process to deepening cognition.

       In a word, the most intrinsic bifurcation differing from the classical statement or the most essential character would be: The entire foundation to make all the inferences is never some special formula but the different idealized convictions on the specially described material object – particle system.

       Not impossibly announcing, it is hard to avoid forms of limitations presented in the cognition progress of a single person who forms the cognition while the capability belonging to a person is rather limited. The recognition on cognition must involve the unremitting self-reflection on the reflection. Especially, to the writer who is not a professional researcher on fluid dynamics, the knowledge on current situation of fluid dynamics researching is rather insufficient and then, a lot of partialities, insufficiencies, improprieties, and even strict wrong may present in these related arguments and then the writer is honestly waited people to correct all of these.

Yang Benluo

Autumn 2001

References of introduction

[1] Shi XunGang, Turbulence, Tientsin (in Chinese) Universe. Press, 1994

[2] Hu Fei, Turbulence, interruptions and gas boundary layer, (in Chinese) Science Press, Beijing, 1995

[3] S. P. Parker, Encyclopedia of physics, McGraw-Hill Comp. 1983

[4] L. D. Landau & E. M. Lifshitz, Quantum mechanics, Butterworth-Heinemann, 1997

[5] Paul K. Feyerabend, Against method – Outline of an anarchistic theory of knowledge, Verso, London, 1978

[6] Yang Benluo, Research on some fundamental concepts of classical thermodynamics (in Chinese), Science Press, Beijing, 1996

[7] Yang Benluo, Classical analysis of fluid motion (in Chinese), Science Press, Beijing, 1996

[8] Yang Benluo, Logic self-consistency analyses of theoretical fluid dynamics - philosophical and mathematical thinking originated from turbulent flow (in Chinese), Shanghai JiaoTong University Press, 1998

[9] Yang Benluo, An essential analysis of natural philosophy - the philosophical and mathematical reconsideration of relativity (in Chinese), Shanghai JiaoTong University Press, 2001


[1] 出版社希望笔者相应提供用英文写成的序言。这样，最终付稿前，笔者对于最初写于前年的序言再次做了部分修改。