دانلود کتاب Waves in Flows

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Preface Contents 1 A Priori Estimates from First Principles in Gas Dynamics 1.1 Introduction 1.2 Compensated Integrability 1.2.1 Evolution Problems A Homogeneous Estimate Integrating in Time First 1.3 Applications to Gas Dynamics (I): Euler Equations 1.3.1 Euler Equations for a Compressible Inviscid Fluid 1.3.2 Why Do We Care? 1.3.3 Estimating the Velocity Field 1.3.4 Flows in a Bounded Domain 1.3.5 Relativistic Gas 1.3.6 Flows with External Force 1.4 Applications (II): Kinetic Models 1.4.1 Boltzmann-Like Models The Cauchy Problem An Extra Estimate for Boltzmann-Like Equations 1.4.2 What Should a Dissipative Model Be? 1.4.3 Discrete Velocity Models 1.5 Applications (III): Mean-Field Models 1.5.1 Vlasov-Type Models 1.5.2 The DPT of a Single Vlasov-Type Equation 1.5.3 Genuine Plasmas 1.6 Applications (IV): Molecular Dynamics 1.6.1 Mass–Momentum Tensor of a Single Particle 1.6.2 Long-Range Forces 1.6.3 Hard Spheres References 2 Equatorial Wave–Current Interactions 2.1 Introduction 2.2 Preliminaries 2.3 The Equatorial f-Plane Approximation 2.4 The Equatorial β-Plane Approximation 2.5 An Exact β-Plane Solution (Equatorially Trapped Wave) 2.5.1 Analysis of the Equatorially Trapped Wave Motion 2.5.2 Quantitative Aspects 2.6 The Ocean Flow in the Equatorial Pacific 2.6.1 The El Niño Phenomenon 2.6.2 A Model for the Equatorial Currents 2.6.3 Equatorial Wave–Current Interactions 2.6.4 Linear Wave Theory 2.6.5 Weakly Nonlinear Models References 3 Linear and Nonlinear Equatorial Waves in a Simple Modelof the Atmosphere 3.1 Introduction 3.2 Linear Equatorial Waves 3.3 Weakly Nonlinear Long Equatorial Waves 3.3.1 Long Linear Rossby and Kelvin Waves 3.3.2 Nonlinear Slow Dynamics of Long Waves 3.4 Equatorial Modons 3.5 Equatorial Adjustment: Initial-Value Problem on the Equatorial Beta-Plane 3.6 Brief Summary and Discussion References 4 The Water Wave Problem and Hamiltonian TransformationTheory 4.1 Introduction 4.2 Water Waves and Hamiltonian PDEs 4.2.1 Physical Derivation of the Governing Equations 4.2.2 General Notions on Hamiltonian Systems 4.2.3 Examples of Hamiltonian PDEs Quasilinear Wave Equation Boussinesq System Korteweg–de Vries Equation Nonlinear Schrödinger Equation 4.2.4 Zakharov's Hamiltonian for Water Waves 4.3 Dirichlet–Neumann Operator and Its Analysis 4.3.1 Legendre Transform 4.3.2 Shape Derivative of H 4.3.3 Invariants of Motion 4.3.4 Taylor Expansion of G 4.4 Birkhoff Normal Forms 4.4.1 Significance of the Normal Form 4.4.2 Complex Symplectic Coordinates and Poisson Brackets 4.4.3 Resonances 4.4.4 FormalTransformationTheoryandBirkhoffNormalForm 4.4.5 Solving the Third-Order Cohomological Equation 4.4.6 Normal Forms for Gravity Waves on Infinite Depth Third-Order Normal Form and Burgers' Equation Fourth-Order Normal Form Integrable Birkhoff Normal Form 4.5 Model Equations for Water Waves 4.5.1 Linearized Problem 4.5.2 Non-dimensionalization 4.5.3 Canonical Transformation Theory 4.5.4 Calculus of Transformations Amplitude Scaling Spatial Scaling Surface Elevation-Velocity Coordinates Moving Reference Frame Characteristic Coordinates 4.5.5 Boussinesq and KdV Scaling Limits 4.5.6 Modulational Scaling Limit and the NLS Equation Normal Form Transformation Modulational Ansatz Expansion and Homogenization of Multiscale Functions NLS Equation Reconstruction of the Free Surface 4.6 Initial Value Problems 4.6.1 Local Well-Posedness 4.6.2 Recent Results on Global Well-Posedness for Small Data 4.6.3 Water Waves in a Periodic Geometry 4.7 Numerical Simulation of Surface Gravity Waves 4.7.1 Tanaka's Method for Solitary Waves 4.7.2 High-Order Spectral Method Space Discretization Time Integration 4.7.3 Collision of Solitary Waves References 5 Gravity Wave Propagation in Inhomogeneous Media 5.1 Introduction 5.2 Water Waves 5.2.1 Propagation on Uneven Bottoms: First Order StokesWaves 5.2.2 Second Order Stokes Waves 5.2.3 Propagation in the Presence of Current or Through Porous Media Propagation in the Presence of Current Propagation Through Porous Media 5.3 Wave Scattering: 2D Case 5.3.1 Standing Wave in a Tank: Resonance and Sloshing 5.3.2 Case of Smooth Bathymetries: Sinusoidal Beds Perturbation Method with Multiple-scale Expansion for Sinusoidal Beds of Finite Extend Mild-Slope and Modified Mild-Slope Equations 5.3.3 Case of Abrupt Bathymetries General Expression of the Velocity Potentials Integral Matching Conditions Method 5.3.4 Examples Sloping Beds Sinusoidal Beds Reflection Due to Structures 5.4 Water Focusing: 3D Case 5.4.1 Refraction—Snell—Descartes' Law 5.4.2 Refraction-Diffraction 5.4.3 Diffraction Analytic Solution: Semi-Infinite Dike Channels of Finite Width 5.4.4 Examples Wave Scattering in the Presence of Underwater Mound Wave Scattering by Surface Piercing Structures Wave Scattering by Emerging Porous Media 5.5 Application to Wave Energy Device 5.5.1 Oscillating Water Column 5.5.2 Pressure Oscillation References 6 Physical Models for Flow: Acoustic Interaction 6.1 Introduction 6.2 Fluid Dynamics 6.2.1 Conservation Equations Conservation of Mass Conservation of Momentum Conservation of Energy 6.2.2 Constitutive Equations 6.2.3 Characterization of Flows by Dimensionless Numbers 6.2.4 Vorticity 6.2.5 Towards Acoustics Formulation for Scalar Potential Formulation for Vector Potential 6.3 Acoustics 6.3.1 Wave Equation 6.3.2 Simple Solutions: d'Alembert 6.3.3 Impulsive Sound Sources 6.3.4 Free-Space Green's Functions 6.3.5 Monopoles, Dipoles, and Quadrupoles 6.3.6 Calculation of Acoustic Far Field 6.3.7 Compactness 6.3.8 Solution of Wave Equation Using Green's Function 6.4 Aeroacoustics 6.4.1 Lighthill's Acoustic Analogy 6.4.2 Curle's Theory 6.4.3 Vortex Sound 6.4.4 Perturbation Equations 6.4.5 Comparison of Different Formulations 6.4.6 Acoustic Feedback Mechanisms 6.5 Applications Coupling strategy of flow and acoustics Fluid dynamics Acoustics Conclusions of workflow 6.5.1 Human Phonation 6.5.2 Axial Fan 6.5.3 Cavity at Low Mach Number schoder2020numerical 6.5.4 Cavity at High Mach Number Appendix References