Theory and Applications of Nonviscous Fluid Flows

ISBN-13: 9783642625510 / Angielski / Miękka / 2012 / 295 str.

Radyadour K. Zeytounian

Opis

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

Recenzje

From the reviews of the first edition:

"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, 2003g)

"[...] presents a broad panorama of model problems encountered in nonviscous Newtonian fluid flows." (International Aerospace Abstracts 42/3, 2002)

"This well-organized book can be recommended to students, teachers and researchers with an interest in asymptotic methods and rigorous foundations of nonviscous fluid mechanics." (Zentralblatt MATH, 992/17, 2002)

"This book touches on a number of topics in fluid mechanics at an advanced level. ... I believe the book could be a welcome addition to the bookshelf of anyone working in theoretical fluid mechanics. It would also be a valuable supplemental text for a post-master course in fluid mechanics." (Anthony Leonard, Journal of Fluid Mechanics, Vol. 517, 2004)

Spis treści

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.

Blurb

The purpose of this book is to present a broad panorama of model problems encountered in nonviscous Newtonian fluid flows. This is achieved by investigating the significant features of the solutions of the corresponding equations using the method of asymptotic analysis. The book thereby fills a long-standing gap in the literature by providing researchers working on applied topics in hydro-aerodynamics, acoustics and geophysical fluid flows with exact results, without having to invoke the complex mathematical apparatus necessary to obtain those insights. The benefit of this approach is two-fold: outlining the idea of the mathematical proofs involved suggests methodologies and algorithms for numerical computation, and also often gives useful information regarding the qualitative behaviour of the solutions. This book is aimed at researchers and students alike as it also provides all the necessary basic knowledge about fluid dynamics.