本书将最小熵产生原理和耗散结构理论以及混沌理论应用到河流演变分析中，并运用这些理论研究分析解决一些河流工程中的实际问题。全书共10章，分别为：经典热力学概论；非平衡态热力学基本理论；混沌理论；黏性流体热力学问题；流体最小能耗率原理的数值水槽仿真模拟；基于能耗率与耗散结构和混沌理论的河床演变分析；基于多元时间序列的不同河型混沌特性分析；基于超熵产生的河型稳定判别；最小能耗率原理在渠首引水防沙设计中的应用；基于最小能耗率原理的稳定渠道优化设计。

目录
序
前言
第1章 经典热力学概论 1
1.1 系统及其分类 1
1.2 平衡态与非平衡态 2
1.2.1 状态参量、状态函数和物态方程 2
1.2.2 平衡态、非平衡态和非平衡定态 3
1.3 可逆过程与不可逆过程 4
1.4 热力学基本定律 5
1.5 熵与优选熵原理 6
1.6 涨落、平衡和稳定 7
1.7 对称性与有序和无序 9
1.8 热力学基本方程及平衡判据 10
1.8.1 热力学基本方程 10
1.8.2 平衡判据与稳定性条件 12
1.9 小结 13
第2章 非平衡态热力学基本理论 14
2.1 非平衡态热力学研究简介 14
2.2 开放系统的状态与熵变 15
2.3 局域平衡假设及基本方程 17
2.3.1 局域平衡假设 17
2.3.2 质量守恒方程 18
2.3.3 局域熵平衡方程 19
2.3.4 局域熵产生与广义力和广义流 21
2.4 Lyapunov稳定性理论 22
2.5 近平衡态线性区的最小熵产生理论 24
2.5.1 唯象方程与Onsager倒易关系 24
2.5.2 最小熵产生原理与定态的稳定性 24
2.6 远离平衡态非线性区的耗散结构理论 28
2.6.1 普适发展判据 28
2.6.2 超熵产生 29
2.6.3 耗散结构及其特点 32
2.6.4 耗散结构形成条件 36
2.7 最小熵产生原理等价于最小能耗率原理 37
2.8 最小熵产生原理和耗散结构理论适用范围 38
2.9 小结 39
第3章 混沌理论 41
3.1 混沌研究起源及发展过程 41
3.2 混沌的概念及分类 43
3.3 产生混沌的途径 44
3.4 混沌的基本特征 46
3.5 识别混沌的几种常用方法 47
3.5.1 相图法 48
3.5.2 分频采样 48
3.5.3 庞加莱截面 48
3.5.4 相空间重构 49
3.5.5 功率谱分析 51
3.5.6 主分量分析 52
3.5.7 分形维数 53
3.5.8 Lyapunov指数 54
3.5.9 测度熵 55
3.6 耗散结构是混沌的一种特例 57
3.7 小结 58
第4章 黏性流体热力学问题 59
4.1 描述流体运动的两种基本方法 59
4.2 流体运动的三个基本方程 60
4.3 流体的熵平衡方程 65
4.4 流体的能量耗散函数及能耗率 66
4.5 基于广义流和广义力的河流能耗率 69
4.5.1 河流的广义力和广义流 70
4.5.2 河流的能量耗散函数及能耗率 71
4.6 流体最小能耗率原理 71
4.7 小结 73
第5章 流体最小能耗率原理的数值水槽仿真模拟 74
5.1 数值水槽模拟概述 74
5.2 水流运动数值模型 75
5.3 水槽变坡模拟 77
5.4 模型建立、网格划分及边界条件 78
5.5 单位体积水体能耗率及其计算 80
5.6 计算工况 81
5.7 计算结果与分析 82
5.8 小结 84
第6章 基于能耗率与耗散结构和混沌理论的河床演变分析 85
6.1 冲积河流自动调整 85
6.1.1 河流的自动调整功能 85
6.1.2 河流的短期调整与长期调整 86
6.1.3 河流处于相对平衡状态时能耗率最小 87
6.2 影响河床演变因素的权重分析 88
6.2.1 基于信息熵的权重分析 89
6.2.2 基于相关系数法的权重分析 95
6.3 基于最小能耗率原理的河相关系 97
6.4 稳定弯道曲率分析 101
6.5 河型成因分析 103
6.6 不同河型的能耗率及其变化 105
6.7 河型转化中的耗散结构和混沌 110
6.8 小结 111
第7章 基于多元时间序列的不同河型混沌特性分析 113
7.1 河流混沌特性分析方法 113
7.2 河流混沌特性分析实例 114
7.2.1 黄河下游6个河段月宽深比、月径流量和月含沙量实测资料 114
7.2.2 宽深比、径流量和含沙量时间序列的相空间重构 134
7.2.3 宽深比、径流量和含沙量时间序列的混沌特性识别 144
7.2.4 宽深比、径流量和含沙量时间序列的混沌特性加权平均 156
7.3 小结 157
第8章 基于超熵产生的河型稳定判别 158
8.1 超熵产生与超能耗率 158
8.2 河型稳定判据 159
8.3 不同河型稳定性分析 163
8.4 小结 167
第9章 最小能耗率原理在渠首引水防沙设计中的应用 168
9.1 低坝（闸）引水渠首泄洪冲沙闸宽度的计算 168
9.1.1 泄洪冲沙闸的布置及其作用 169
9.1.2 泄洪冲沙闸宽度计算方法 170
9.2 弯道式引水渠首中弯道的优化设计 172
9.2.1 引水弯道优化设计数学模型 173
9.2.2 优化计算结果及验证 175
9.3 小结 176
基于最小能耗率原理的稳定渠道优化设计 177
10.1 稳定渠道的类型及适用条件 177
10.2 稳定渠道优化设计目标函数 178
10.3 渠道不淤流速与不冲流速 179
10.3.1 渠道水流挟沙力 179
10.3.2 渠道不淤流速 181
10.3.3 渠道不冲流速 182
10.4 不冲不淤平衡渠道优化设计 183
10.5 冲淤平衡渠道优化设计 187
10.6 小结 191
参考文献 192
附录A 矩阵概念 200
附录B 矢量、张量与场论基础 204
B.1 矢量 204
B.2 张量 207
B.3 场论 212
附录C 泛函和变分初步 217
C.1 泛函 217
C.2 变分 220
ContentsContents
Preface
Introduction
Chapter 1 Introduction to classical thermodynamics 1
1.1 System and its classification 1
1.2 Equilibrium and non-equilibrium states 2
1.2.1 State parameter, state function and equation of state 2
1.2.2 Equilibrium, non-equilibrium states and non-equilibrium steady state 3
1.3 Reversible and irreversible processes 4
1.4 Basic laws of thermodynamics 5
1.5 Entropy and the principle of maximum entropy 6
1.6 Fluctuation, equilibrium and stability 7
1.7 Symmetry, order and disorder 9
1.8 Basic equations of thermodynamics and criterion of equilibrium 10
1.8.1 Basic equations of thermodynamics 10
1.8.2 Criterion of equilibrium and stability condition 12
1.9 Summary 13
Chapter 2 Basic theory of non-equilibrium thermodynamics 14
2.1 Brief introduction to the study of non-equilibrium thermodynamics 14
2.2 State and entropy change of open system 15
2.3 Local equilibrium assumption and basic equations 17
2.3.1 Local equilibrium assumption 17
2.3.2 Mass conservation equation 18
2.3.3 Local entropy equilibrium equation 19
2.3.4 Local entropy production, generalized forces and generalized flows 21
2.4 Lyapunov’s stability theory 22
2.5 Theory of minimum entropy production in linear regions near equilibrium 24
2.5.1 Phenomenological equation and Onsager reciprocal relations 24
2.5.2 Theories of minimum entropy generation and the stability of steady state 24
2.6 Dissipative structure theory in nonlinear regions far from equilibrium 28
2.6.1 Pervasive development criteria 28
2.6.2 Excess entropy production 29
2.6.3 Dissipative structure and characteristics 32
2.6.4 Dissipative structure formation condition 36
2.7 The minimum entropy production equivalent to the minimum energy dissipation rate 37
2.8 Application scope of the theories of minimum entropy generation and dissipative structure 38
2.9 Summary 39
Chapter 3 Theory of chaos 41
3.1 Origin and development of chaos 41
3.2 Concepts and classification of chaos 43
3.3 Approaches of generating chaos 44
3.4 Basic features of chaos 46
3.5 Several common methods of identifying chaos 47
3.5.1 Phase diagram method 48
3.5.2 Stroboscopic sampling method 48
3.5.3 Poincaré section 48
3.5.4 Phase space reconstruction 49
3.5.5 Power spectrum analysis 51
3.5.6 Principal component analysis 52
3.5.7 Fractal dimension 53
3.5.8 Lyapunov exponent 54
3.5.9 Measure entropy 55
3.6 Dissipative structure: A special case of chaos 57
3.7 Summary 58
Chapter 4 Thermodynamic problems of viscous fluids 59
4.1 Two basic methods of describing fluid motion 59
4.2 Basic equations of fluid motion 60
4.3 Entropy balance equation of fluid 65
4.4 Energy dissipation function and energy dissipation rate of fluid 66
4.5 Energy dissipation rate of rivers based on generalized flows and generalized forces 69
4.5.1 Generalized flows and generalized forces of rivers 70
4.5.2 Energy dissipation function and energy dissipation rate of rivers 71
4.6 Principle of minimum energy dissipation rate of fluid 71
4.7 Summary73
Chapter 5 Numerical flume simulation of minimum energy dissipation rate of fluid 74
5.1 Overview of numerical flume simulation 74
5.2 Numerical models of fluid motion 75
5.3 Simulation of flume slope variation 77
5.4 Model setup, grid division and boundary conditions 78
5.5 Energy dissipation rate of unit volume of water and its calculation 80
5.6 Calculation conditions 81
5.7 Calculation results and analysis 82
5.8 Summary 84
Chapter 6 Analysis of river evolution based on energy dissipation rate and dissipative structure and chaos 85
6.1 Self-adjustment of alluvial rivers 85
6.1.1 Self-adjustment function of rivers 85
6.1.2 Short-term and long-term adjustment of rivers 86
6.1.3 Energy dissipation rate reached minimum at a relatively balanced state of rivers 87
6.2 Weight analysis of factors affecting river evolution 88
6.2.1 Weight analysis based on information entropy 89
6.2.2 Weight analysis based on correlation coefficient method 95
6.3 River facies relation based on minimum energy dissipation rate 97
6.4 Curvature analysis of stable bend 101
6.5 Cause analysis of river pattern 103
6.6 Energy dissipation rate and its variation of different river patterns 105
6.7 Dissipative structure and chaos in the transformation of river patterns 110
6.8 Summary 111
Chapter 7 Analysis of chaos characteristics of different river patterns based on multivariate time series 113
7.1 Analysis methods of the chaos characteristics of rivers 113
7.2 Examples 114
7.2.1 Measured data of monthly width-depth ratio, monthly runoff and monthly sediment concentration of 6 reaches in the lower Yellow River 114
7.2.2 Phase space reconstruction of width-depth ratio, runoff and sediment concentration time series 134
7.2.3 Chaos characteristics recognition of width-depth ratio, runoff and sediment concentration time series 144
7.2.4 Chaos characteristics weighted average of width-depth ratio, runoff and sediment concentration time series 156
7.3 Summary 157
Chapter 8 Discriminant of river pattern stability based on excess entropy production 158
8.1 Excess entropy production and excess energy dissipation rate 158
8.2 Stability criteria of river patterns 159
8.3 Analysis of stability of different river patterns 163
8.4 Summary 167
Chapter 9 Application of minimum energy dissipation rate in headwork design for water diversion and sand prevention 168
9.1 Calculation of the scouring sluice width in low dam diversion headworks 168
9.1.1 Arrangement and function of the scouring sluice 169
9.1.2 Calculation method of the scouring sluice width 170
9.2 Optimization design of the bend in bend diversion headworks 172
9.2.1 Optimal designed mathematical model of diversion curve 173
9.2.2 Optimized results and validation 175
9.3 Summary 176
Chapter 10 Optimal design of stable channel based on minimum energy dissipation rate 177
10.1 Types of stable channels and their application conditions 177
10.2 Objective function for optimal design of stable channels 178
10.3 Non-silting velocity and non-eroding velocity of channels 179
10.3.1 Channel flow sediment capacity 179
10.3.2 Non-silting velocity of channels 181
10.3.3 Non-eroding velocity of channels 182
10.4 Optimal design of non-silting and non-eroding channels 183
10.5 Optimal design of equilibrium of eroding and silting channels 187
10.6 Summary 191
References 192
Appendix A : Concepts of matrix 200
Appendix B : Vector , tensor and field basis 204
B.1 Vector 204
B.2 Tensor 207
B.3 Field theory 212
Appendix C : Preliminary functional and variational calculus 217
C.1 Functional 217
C.2 Variational calculus 220