| Introduction |
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xi | |
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Part I Bases of Hydrodynamics |
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1 | (128) |
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Chapter 1 Equations of Motion |
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3 | (70) |
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3 | (14) |
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1.2 Navier--Stokes Equations |
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17 | (12) |
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1.3 Kinetic Equations and Gas Dynamics |
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29 | (41) |
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70 | (3) |
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Chapter 2 Gravity Waves and Solitons |
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73 | (12) |
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2.1 Wave Equation and Free Surface Gravity Waves |
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73 | (5) |
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2.2 Waves in Dispersive Media |
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78 | (2) |
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2.3 Waves at a Density Interface Between Liquids of Different Densities |
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80 | (4) |
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84 | (1) |
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Chapter 3 Thermodynamics of Fluids |
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85 | (16) |
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85 | (6) |
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3.2 Thermodynamical Properties of Fluids and Gases |
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91 | (8) |
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99 | (2) |
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101 | (28) |
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4.1 One-Dimensional Fluidodynamics and Rankine--Hugoniot Conditions |
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101 | (16) |
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4.2 Weak Shocks and the Boltzmann Equation |
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117 | (10) |
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127 | (2) |
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Part II Stability and Instabilities in Fluidodynamics |
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129 | (74) |
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Chapter 5 Instabilities in Fluidodynamics and Its Consequences |
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131 | (32) |
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5.1 An Introduction to Thermal Convection |
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131 | (4) |
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5.2 Linear Analysis and Normal Modes |
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135 | (11) |
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5.3 Classical Types of Hydrodynamical Instabilities |
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146 | (16) |
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162 | (1) |
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Chapter 6 Classical Turbulence in Fluid Dynamics |
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163 | (40) |
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6.1 Introduction to Classical Turbulence |
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163 | (8) |
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6.2 The Homogeneous Turbulence and Its Spectrum |
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171 | (18) |
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6.3 Direct Numerical Simulation of Turbulence |
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189 | (12) |
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201 | (2) |
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Part III Coherent Hydrodynamic Structures |
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203 | (36) |
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Chapter 7 Vortex Dynamics on the Plane |
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205 | (12) |
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7.1 Joyce--Montgomery Equation for Vorticity |
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205 | (4) |
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7.2 Vortex Systems with Negative Temperature |
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209 | (3) |
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7.3 Kinetic Origin of Multivortex Systems |
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212 | (3) |
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215 | (2) |
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Chapter 8 Poisson Systems in Hydrodynamics |
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217 | (12) |
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8.1 Poisson Systems and States of Relative Equilibrium |
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217 | (3) |
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8.2 Young Measures in Hydrodynamics |
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220 | (3) |
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8.3 Equilibrium States in Statistical Mechanics of the Euler Equation and Variation of Functionals in Poisson Systems |
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223 | (4) |
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227 | (2) |
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Chapter 9 Introduction of Metric Structure in Hydrodynamic Systems |
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229 | (10) |
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9.1 Lagrangian and Hamiltonian Formalism of the Description of the Hydrodynamic System in Terms of Monge Potentials |
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230 | (2) |
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9.2 The Canonical Connections of the Hamiltonian Space |
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232 | (2) |
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9.3 The Deviation of Geodesies on the Monge Manifolds |
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234 | (3) |
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237 | (2) |
| Appendices |
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239 | (2) |
| Appendix A Chaplygin's Gas |
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241 | (6) |
| Appendix B Richtmyer--Meshkov Instability |
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247 | (8) |
| Appendix C Instabilities and Turbulence in Astrophysics |
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255 | (16) |
| References |
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271 | (10) |
| Index |
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281 | |
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