目錄
序
前言
第1章 經(jīng)典熱力學(xué)概論 1
1.1 系統(tǒng)及其分類 1
1.2 平衡態(tài)與非平衡態(tài) 2
1.2.1 狀態(tài)參量、狀態(tài)函數(shù)和物態(tài)方程 2
1.2.2 平衡態(tài)、非平衡態(tài)和非平衡定態(tài) 3
1.3 可逆過程與不可逆過程 4
1.4 熱力學(xué)基本定律 5
1.5 熵與最大熵原理 6
1.6 漲落、平衡和穩(wěn)定 7
1.7 對稱性與有序和無序 9
1.8 熱力學(xué)基本方程及平衡判據(jù) 10
1.8.1 熱力學(xué)基本方程 10
1.8.2 平衡判據(jù)與穩(wěn)定性條件 12
1.9 小結(jié) 13
第2章 非平衡態(tài)熱力學(xué)基本理論 14
2.1 非平衡態(tài)熱力學(xué)研究簡介 14
2.2 開放系統(tǒng)的狀態(tài)與熵變 15
2.3 局域平衡假設(shè)及基本方程 17
2.3.1 局域平衡假設(shè) 17
2.3.2 質(zhì)量守恒方程 18
2.3.3 局域熵平衡方程 19
2.3.4 局域熵產(chǎn)生與廣義力和廣義流 21
2.4 Lyapunov穩(wěn)定性理論 22
2.5 近平衡態(tài)線性區(qū)的最小熵產(chǎn)生理論 24
2.5.1 唯象方程與Onsager倒易關(guān)系 24
2.5.2 最小熵產(chǎn)生原理與定態(tài)的穩(wěn)定性 24
2.6 遠(yuǎn)離平衡態(tài)非線性區(qū)的耗散結(jié)構(gòu)理論 28
2.6.1 普適發(fā)展判據(jù) 28
2.6.2 超熵產(chǎn)生 29
2.6.3 耗散結(jié)構(gòu)及其特點 32
2.6.4 耗散結(jié)構(gòu)形成條件 36
2.7 最小熵產(chǎn)生原理等價于最小能耗率原理 37
2.8 最小熵產(chǎn)生原理和耗散結(jié)構(gòu)理論適用范圍 38
2.9 小結(jié) 39
第3章 混沌理論 41
3.1 混沌研究起源及發(fā)展過程 41
3.2 混沌的概念及分類 43
3.3 產(chǎn)生混沌的途徑 44
3.4 混沌的基本特征 46
3.5 識別混沌的幾種常用方法 47
3.5.1 相圖法 48
3.5.2 分頻采樣 48
3.5.3 龐加萊截面 48
3.5.4 相空間重構(gòu) 49
3.5.5 功率譜分析 51
3.5.6 主分量分析 52
3.5.7 分形維數(shù) 53
3.5.8 Lyapunov指數(shù) 54
3.5.9 測度熵 55
3.6 耗散結(jié)構(gòu)是混沌的一種特例 57
3.7 小結(jié) 58
第4章 黏性流體熱力學(xué)問題 59
4.1 描述流體運動的兩種基本方法 59
4.2 流體運動的三個基本方程 60
4.3 流體的熵平衡方程 65
4.4 流體的能量耗散函數(shù)及能耗率 66
4.5 基于廣義流和廣義力的河流能耗率 69
4.5.1 河流的廣義力和廣義流 70
4.5.2 河流的能量耗散函數(shù)及能耗率 71
4.6 流體最小能耗率原理 71
4.7 小結(jié) 73
第5章 流體最小能耗率原理的數(shù)值水槽仿真模擬 74
5.1 數(shù)值水槽模擬概述 74
5.2 水流運動數(shù)值模型 75
5.3 水槽變坡模擬 77
5.4 模型建立、網(wǎng)格劃分及邊界條件 78
5.5 單位體積水體能耗率及其計算 80
5.6 計算工況 81
5.7 計算結(jié)果與分析 82
5.8 小結(jié) 84
第6章 基于能耗率與耗散結(jié)構(gòu)和混沌理論的河床演變分析 85
6.1 沖積河流自動調(diào)整 85
6.1.1 河流的自動調(diào)整功能 85
6.1.2 河流的短期調(diào)整與長期調(diào)整 86
6.1.3 河流處于相對平衡狀態(tài)時能耗率最小 87
6.2 影響河床演變因素的權(quán)重分析 88
6.2.1 基于信息熵的權(quán)重分析 89
6.2.2 基于相關(guān)系數(shù)法的權(quán)重分析 95
6.3 基于最小能耗率原理的河相關(guān)系 97
6.4 穩(wěn)定彎道曲率分析 101
6.5 河型成因分析 103
6.6 不同河型的能耗率及其變化 105
6.7 河型轉(zhuǎn)化中的耗散結(jié)構(gòu)和混沌 110
6.8 小結(jié) 111
第7章 基于多元時間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 河流混沌特性分析實例 114
7.2.1 黃河下游6個河段月寬深比、月徑流量和月含沙量實測資料 114
7.2.2 寬深比、徑流量和含沙量時間序列的相空間重構(gòu) 134
7.2.3 寬深比、徑流量和含沙量時間序列的混沌特性識別 144
7.2.4 寬深比、徑流量和含沙量時間序列的混沌特性加權(quán)平均 156
7.3 小結(jié) 157
第8章 基于超熵產(chǎn)生的河型穩(wěn)定判別 158
8.1 超熵產(chǎn)生與超能耗率 158
8.2 河型穩(wěn)定判據(jù) 159
8.3 不同河型穩(wěn)定性分析 163
8.4 小結(jié) 167
第9章 最小能耗率原理在渠首引水防沙設(shè)計中的應(yīng)用 168
9.1 低壩（閘）引水渠首泄洪沖沙閘寬度的計算 168
9.1.1 泄洪沖沙閘的布置及其作用 169
9.1.2 泄洪沖沙閘寬度計算方法 170
9.2 彎道式引水渠首中彎道的優(yōu)化設(shè)計 172
9.2.1 引水彎道優(yōu)化設(shè)計數(shù)學(xué)模型 173
9.2.2 優(yōu)化計算結(jié)果及驗證 175
9.3 小結(jié) 176
基于最小能耗率原理的穩(wěn)定渠道優(yōu)化設(shè)計 177
10.1 穩(wěn)定渠道的類型及適用條件 177
10.2 穩(wěn)定渠道優(yōu)化設(shè)計目標(biāo)函數(shù) 178
10.3 渠道不淤流速與不沖流速 179
10.3.1 渠道水流挾沙力 179
10.3.2 渠道不淤流速 181
10.3.3 渠道不沖流速 182
10.4 不沖不淤平衡渠道優(yōu)化設(shè)計 183
10.5 沖淤平衡渠道優(yōu)化設(shè)計 187
10.6 小結(jié) 191
參考文獻(xiàn) 192
附錄A 矩陣概念 200
附錄B 矢量、張量與場論基礎(chǔ) 204
B.1 矢量 204
B.2 張量 207
B.3 場論 212
附錄C 泛函和變分初步 217
C.1 泛函 217
C.2 變分 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