| The starred sections are self-contained and may be omitted at a first reading. Series Preface 1 Introduction 2 The Equations of Inviscid Compressible Flow 2.1 The Field Equations 2.2 Initial and Boundary Conditions 2.3 Vorticity and Irrotationality 2.3.1 Homentropic Flow 2.3.2 Incompressible Flow Exercises 3 Models for Linear Wave Propagation 3.1 Acoustics 3.2 Surface Gravity Waves in Incompressible Flow 3.3 Inertial Waves 3.4 Waves in Rotating Incompressible Flows 3.5 Isotropic Electromagnetic and Elastic Waves Exercises 4 Theories for Linear Waves 4.1 Wave Equations and Hyperbolicity 4.2 Fourier Series, Eigenvalues, and Resonance 4.3 Fourier Integrals and the Method of Stationary Phase 4.4 Dispersion and Group Velocity 4.4.1 Dispersion Relations 4.4.2 Other Approaches to Group Velocity 4.5 The Frequency Domain 4.5.1 Homogeneous Media 4.5.2 Scattering Problems in Homogeneous Media 4.5.3 Inhomogeneous Media 4.6 Stationary Waves 4.6.1 Stationary Surface Waves on a Running Stream 4.6.2 Steady Flow in Slender Nozzles 4.6.3 Compressible Flow past Thin Wings 4.6.4 Compressible Flow past Slender Bodies 4.7 High-frequency Waves 4.7.1 The Eikonal Equation 4.7.2 Ray Theory 4.8 Dimensionality and the Wave Equation Exercises 5 Nonlinear Waves in Fluids 5.1 Introduction 5.2 Models for Nonlinear Waves 5.2.1 One-dimensional Unsteady Gasdynamics 5.2.2 Two-dimensional Steady Homentropic Gasdynamics . 5.2.3 Shallow Water Theory 5.2.4 Nonlinearity and Dispersion 5.3 Smooth Solutions for Nonlinear Waves 5.3.1 The Piston Problem for One-dimensional Unsteady Gasdynamies 5.3.2 Prandtl-Meyer Flow 5.3.3 The Dam Break Problem 5.4 The Hodograph Transformation Exercises 6 Shock Waves 6.1 Discontinuous Solutions 6.1.1 Introduction to Weak Solutions 6.1.2 Rankine-Hugoniot Shock Conditions 6.1.3 Shocks in Two-dimensional Steady Flow 6.1.4 Jump Conditions in Shallow Water 6.2 Other Flows involving Shock Waves 6.2.1 Shock Tubes 6.2.2 Oblique Shock Interactions 6.2.3 Steady Quasi-one-dimensional Gas Flow 6.2.4 Shock Waves with Chemical Reactions 6.2.5 Open Channel Flow 6.3 Further Limitations of Linearized Gasdynamics 6.3.1 Transonic Flow 6.3.2 The Far Field for Flow past a Thin Wing 6.3.3 Non-equilibrium Effects 6.3.4 Hypersonic Flow Exercises 7 Epilogue References. Index |
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