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　　分類: 图书,进口原版书,科学与技术 Science & Techology ,

作者： Tian-Quan Chen 著

出 版 社： Penguin

出版时间： 2003-12-1字数：版次： 1页数： 420印刷时间： 2003/12/01开本：印次： 1纸张： 胶版纸I S B N ： 9789812383785包装： 精装内容简介

This book presents the construction of an asymptotic technique for solving the Liouville equation, which is to some degree an analogue of the Enskog–Chapman technique for solving the Boltzmann equation. Because the assumption of molecular chaos has been given up at the outset, the macroscopic variables at a point, defined as arithmetic means of the corresponding microscopic variables inside a small neighborhood of the point, are random in general. They are the best candidates for the macroscopic variables for turbulent flows. The outcome of the asymptotic technique for the Liouville equation reveals some new terms showing the intricate interactions between the velocities and the internal energies of the turbulent fluid flows, which have been lost in the classical theory of BBGKY hierarchy.

目录

Foreword

Preface

1 Introduction

1.1 Historical Background

1.2 Outline of the Book

2 H-Functional

2.1 Hydrodynamic Random Fields

2.2 H-Functional

3 H-Functional Equation

3.1 Derivation of H-Functional Equation

3.2 H-Functional Equation

3.3 Balance Equations

3.4 Reformulation

4 K-Functional

4.1 Definition of K-Functional

5 Some Useful Formulas

5.1 Some Useful Formulas

5.2 A Remark on H-Functional Equation

6 Turbulent Gibbs Distributions

6.1 Asymptotic Analysis for Liouville Equation

6.2 Turbulent Gibbs Distributions

6.3 Gibbs Mean

7 Euler K-Functional Equation

7.1 Expressions of B2 and B3

7.2 Euler K-Functional Equation

7.3 Reformulation

7.4 Special Cases

7.5 Case of Deterministic Flows

8 Functionals and Distributions

8.1 K-Functionals and Turbulent Gibbs Distributions

8.2 Turbulent Gibbs Measures

8.3 Asymptotic Analysis

9 Local Stationary Liouville Equation

9.1 Gross Determinism

9.2 Temporal Part of Material Derivative of TN

9.3 Spatial Part of Material Derivative of TN

9.4 Stationary Local Liouville equation

10 Second Order Approximate Solutions

10.1 Case of Reynolds-Gibbs Distributions

10.2 A Poly-spherical Coordinate System

10.3 A Solution to the Equation (10.24)1

……

11 A Finer K-Functional Equation

12 Conclusions

A Some Facts About Spherical Harmonics

Bibliography

Index

 

 

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