Theory and applications of nonviscous fluid flows
著者
書誌事項
Theory and applications of nonviscous fluid flows
（Physics and astronomy online library）
Springer, c2002
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注記
Includes bibliographical references (p. [281]-290) and index
内容説明・目次
内容説明
From the reviews: "Researchers in fluid dynamics and applied mathematics will enjoy this book for its breadth of coverage, hands-on treatment of important ideas, many references, and historical and philosophical remarks." Mathematical Reviews
目次
1. Fluid Dynamic Limits of the Boltzmann Equation.- 1.1 The Boltzmann Equation.- 1.2 The Fluid Dynamic Limits.- 1.2.1 Hilbert Expansion.- 1.2.2 The Entropy Approach.- 1.2.3 Some Complementary Remarks.- 1.3 Comments.- 2. From Classical Continuum Theory to Euler Equations via N-S-F Equations.- 2.1 Newtonian Fluids.- 2.1.1 Rate of Strain and Stress Tensors.- 2.1.2 Constitutive Relations for a Newtonian Fluid.- 2.1.3 Equations of State: Perfect Gas and Expansible Liquid.- 2.2 Partial Differential Equations for the Motion of Any Continuum.- 2.3 N-S-F Equations.- 2.3.1 For a Perfect Gas.- 2.3.2 For an Expansible Liquid.- 2.4 Dimensionless N-S-F Equations.- 2.4.1 Nondimensional Form of the N-S-F Equations for a Perfect Gas.- 3. Short Presentation of Asymptotic Methods and Modelling.- 3.1 Method of Strained Coordinates.- 3.2 Method of Matched Asymptotic Expansions.- 3.3 Multiple Scale Method.- 3.3.1 Homogenization Method.- 3.4 Flow with Variable Viscosity: An Asymptotic Model.- 3.4.1 The Associated Three Limiting Processes.- 3.4.2 Interaction Between the BL and the LVL.- 3.5 Low Mach Number Flows: Weakly Nonlinear Acoustic Waves.- 3.5.1 Steichen Equation for an Eulerian Irrotational Flow.- 3.5.2 Unsteady-State One-Dimensional Case.- 3.5.3 Burgers Equation for the Far Field in the Dissipative Case.- 4. Various Forms of Euler Equations and Some Hydro-Aerodynamics Problems.- 4.1 Barotropic Inviscid Fluid Flow.- 4.2 Bernoulli Equation and Potential Flows.- 4.3 D'Alembert Paradox and Kutta-Joukowski-Villat Condition.- 4.3.1 More Concerning the K-J-V Condition.- 4.4 Potential Flows and Water Waves.- 4.4.1 Formulation of the Water-Wave Problem.- 4.4.2 From Cauchy and Poisson to Airy and Stokes.- 4.4.3 Boussinesq and KdV Equations.- 4.4.4 Soliton Dynamics, KP, NLS, and NLS-Poisson Equations.- 4.5 Compressible Eulerian Baroclinic Fluid Flow.- 4.5.1 Lagrangian Invariants.- 4.5.2 Clebsch's and Weber's Transformations. Hamiltonian Form and Cauchy's Integral.- 4.5.3 Vector Field Frozen into the Medium and Fridman's Theorem.- 4.5.4 A Variational Principle.- 4.5.5 The Formation of Vortices and Bjerknes' Theorem.- 4.5.6 Various Forms of Euler Equations.- 4.6 Isochoric Fluid Flows.- 4.6.1 From Isochoric Fluid Flow to Incompressible Fluid Flow.- 4.6.2 Unsteady-State 2-D Case.- 4.6.3 Steady-State 2-D Case.- 4.6.4 Weakly Nonlinear Long Internal Waves in Stratified Flows.- 4.7 Isentropic Fluid Flow and the Steichen Equation.- 4.7.1 Isentropic Euler Equations.- 4.7.2 The Steichen Equation for the Velocity Potential.- 4.8 Steady Euler Equations and Stream Functions.- 4.8.1 2-D Case.- 4.8.2 3-D Adiabatic Steady-State Flows.- 5. Atmospheric Flow Equations and Lee Waves.- 5.1 Euler Equations for Atmospheric Motions.- 5.1.1 Generalisation of the Bjerknes' Theorem. Influence of the Coriolis Acceleration.- 5.2 The Meteorological "Primitive" Kibel Equations.- 5.2.1 The f0-Plane Approximation.- 5.2.2 The Primitive (Kibel) Equations.- 5.2.3 The Quasi-Geostrophic Model Equation.- 5.2.4 Adjustment to Geostrophy. Formulation of the Initial Condition for the QG Equation (5.49).- 5.3 The Boussinesq Inviscid Equations.- 5.3.1 The Standard Atmosphere.- 53.2 Asymptotic Derivation of Inviscid Boussinesq Equations.- 5.3.3 Steady Boussinesq Case.- 5.3.4 From Isochoric Equations to Boussinesq Equations.- 5.4 Isochoric Lee Waves.- 5.4.1 Steady-State 2-D Model Problems.- 5.4.2 Isochoric 2-D Steady-State Lee Waves.- 5.5 Boussinesq Lee Waves.- 6. Low Mach Number Flow and Acoustics Equations.- 6.1 Euler Incompressible Limit Equations.- 6.1.1 Equation for the Temperature Perturbation.- 6.2 Equations of Acoustics.- 6.2.1 External Aerodynamics.- 6.2.2 Internal Aerodynamics.- 6.2.3 The Singular Nature of the Far Field.- 7. Turbo-Machinery Fluid Flow.- 7.1 Various Facets of an Asymptotic Theory.- 7.2 Through-Flow Model.- 7.3 Flow Analysis at the Leading/Trailing Edges of a Row.- 7.4 Complementary Remarks.- 7.4.1 A Simple "Two-Stream Function" Approach.- 8. Vortex Sheets and Shock Layer Phenomena.- 8.1 The Concept of Discontinuity.- 8.1.1 Entropy and Vorticity Introduced Behind a Shock.- 8.2 Jump Relations Associated with a Conservation Law.- 8.2.1 Normal Shock.- 8.2.2 Oblique Shock.- 8.3 The Structure of the Shock Layer.- 8.3.1 A Simple Description of the Structure of the Taylor Shock Layer.- 8.4 Some Properties of the Vortex Sheet.- 8.4.1 The Guiraud-Zeytounian "Rolled-Up Vortex Sheet" Theory.- 9. Rigorous Mathematical Results.- 9.1 Well-Posedness of Eulerian Fluid Flows.- 9.1.1 The Well-Posedness of Eulerian Incompressible Fluid Flow.- 9.1.2 The Well-Posedness of Eulerian Compressible Fluid Flow.- 9.1.3 Solvability of Eulerian Fluid Flow.- 9.1.4 The Cauchy-Kowalevski Theorem.- 9.1.5 Stability-Instability Concept.- 9.2 Existence, Regularity, and Uniqueness Results.- 9.2.1 Water Waves and Solitary Waves.- 9.2.2 Motion of a Compressible Inviscid Fluid.- 9.2.3 The Incompressible Limit of Compressible Euler Equations.- 9.2.4 More Recent Rigorous Results.- References.
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