Fundamental of Ocean Dynamics (eBook)

Front Cover 1
Fundamentals of Ocean Dynamics 4
Copyright Page 5
CONTENTS 8
PREFACE TO 1973 EDITION 6
PREFACE TO ENGLISH EDITION 1977 7
Chapter 1. Statics. Thermodynamics of equilibrium states 12
1.1 Entropy 12
1.2 Equilibrium processes 17
1.3 Thermodynamic potentials 21
1.4 Sea water as a two-component solution 23
1.5 Entropy, internal energy and chemical potential of sea water 25
1.6 Adiabatic temperature gradient and compressibility of sea water 29
1.7 Thermodynamic inequalities 33
1.8 Conditions of equilibrium of sea water 35
1.9 Condition for the absence of convection. Väisälä frequency 39
Comment on Chapter 1 41
Chapter 2. Dynamics, Thermodynamics of irreversible processes 42
2.1 Thermodynamic parameters in a non-equilibrium state 42
2.2 Equations of conservation of mass 43
2.3 Equations of motion 46
2.4 Equations of angular momentum 48
2.5 Equation of conservation of energy 49
2.6 Equations for mechanical and internal energy 51
2.7 Equation of entropy transfer 53
2.8 The basic propositions of the thermodynamics of irreversible processes 55
2.9 The relationship between the viscous stress tensor and the strain rate tensor 56
2.10 The relationship between fluxes of heat and salt and temperature, pressure and salinity gradients 57
Comment on Chapter 2 59
Chapter 3. Wave motion in the ocean 60
3.1 Basic equations 60
3.2 Separation of variables 65
3.3 Analysis of the simplest cases 67
3.4 The eigenvalue curves for Problem V 77
3.5 The eigenvalue curves of Problem H 87
3.6 Classification of free oscillations 95
3.7 Some approximations and their analysis 98
3.8 Approximate analysis of Problem H. The concept of the ß-plane 101
3.9 Problem of forced wave motions 109
Comment on Chapter 3 112
Chapter 4. Equations of the theory of ocean currents and their properties 114
4.1 Equation of evolution of potential vorticity 114
4.2 Boussinesq’s approximation 117
4.3 Averaging of basic equations 120
4.4 Equation for turbulent energy 122
4.5 The basic equations in spherical coordinates 124
4.6 Coefficients of turbulent exchange 126
4.7 Boundary conditions 129
4.8 Quasi-static approximation 131
4.9 Geostrophic motion 134
Comment on Chapter 4 136
Chapter 5. Ekman theory, Wind-driven currents in a homogeneous ocean 138
5.1 Pure drift current 138
5.2 The basic equations of Ekman theory 140
5.3 Vertical structure of the flow Ekman boundary layers
5.4 General method of solution of problem 145
5.5 Certain very simple solutions 148
5.6 Western boundary current 150
5.7 Effect of bottom relief on boundary current 156
Comment on Chapter 5 163
Chapter 6. Two-dimensional models of ocean currents 164
6.1 Method of total flows 164
6.2 General analysis of a two-dimensional model 167
6.3 Viscous boundary layer 172
6.4 Inertial boundary layer 178
6.5 Inertial — viscous boundary layer 183
6.6 The boundary layer for large and small Reynolds numbers 191
6.7 Non-stationary boundary layer 197
Comment on Chapter 6 202
Chapter 7. Three-dimensional models of ocean currents 204
7.1 Boundary currents in a homogeneous fluid 204
7.2 Simplest linear model of thermocline 213
7.3 A non-linear model of the thermocline 220
Comment on Chapter 7 223
Appendix A. Elements of tensor analysis 224
A.1 Curvilinear coordinates 224
A.2 Transformation of coordinates 226
A.3 Tensors 228
A.4 Examples of simple tensors 230
A.5 Isotropic and axisymmetric tensors 232
A.6 Differentiation of tensors 233
A.7 Invariant differential operators 235
A.8 Curvature tensor 237
A.9 Basic formulae 239
Comment on Appendix A 242
Appendix B. On matching of asymptotic expansions 244
Comment on Appendix B 250
Bibliography 252
Subject index 258