Waves and compressible flow波与可压缩流

作者简介

This books aims to provide students and rsearchers with a basis for understanding the wide range of wave phenomena with which any mathematician may be confronted in applications. Compressible flow is the main focus of the book however the authors show how wave phenomena in electromagentism and solid mechanics can be treated using similar mathematical methods. This book originated from a course at Oxford University and previous book by H Ockendon and R Taylor entitled Inviscid Fluid Flows. This monograph has been retitled and revised throughly to reflect scientific interest. The book has exercises at end of each chapter and should appeal to senior undergraduate and graduate students interested in fluid mechanics.

书籍目录

The starred sections are self-contained and may be omitted at a first reading.Series Preface1 Introduction2 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  Exercises3 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　Exercises4 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  Exercises5 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  Exercises6 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  Exercises7  EpilogueReferences.Index

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