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Theory and Applications of Nonviscous Fluid Flows - R. Kh. Zeytounian

Theory and Applications of Nonviscous Fluid Flows

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Published: June 2009
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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.

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)

Introductionp. 1
Fluid Dynamic Limits of the Boltzmann Equationp. 11
The Boltzmann Equationp. 11
The Fluid Dynamic Limitsp. 12
Hilbert Expansionp. 15
The Entropy A pproachp. 17
Some Complementary Remarksp. 18
Commentsp. 20
From Classical Continuum Theory to Euler Equations via N-S-F Equationsp. 25
Newtonian Fluidsp. 25
Rate of Strain and Stress Tensorsp. 27
Constitutive Relations for a Newtonian Fluidp. 27
Equations of State: Perfect Gas and Expansible Liquidp. 29
Partial Differential Equations for the Motion of Any Continuump. 31
N-S-F Equationsp. 32
For a Perfect Gasp. 32
For an Expansible Liquidp. 33
Dimensionless N-S-F Equationsp. 34
Nondimensional Form of the N-S-F Equations for a Perfect Gasp. 34
A Short Presentation of Asymptotic Methods and Modellingp. 37
Method of Strained Coordinatesp. 39
Method of Matched A symptotic Expansionsp. 39
Multiple Scale Methodp. 42
Homogenization Methodp. 43
Flow with Variable Viscosity: An A symptotic Modelp. 44
The Associated Three Limiting Processesp. 46
Interaction Between the BL and the LVLp. 48
Low Mach Number Flows: Weakly Nonlinear Acoustic Wavesp. 49
Steichen Equation for an Eulerian Irrotational Flowp. 49
Unsteady-State One-Dimensional Casep. 50
Burgers Equation for the Far Field in the Dissipative Casep. 54
Various Forms of Euler Equations and Some Hydro-Aerodynamics Problemsp. 61
Barotropic Inviscid Fluid Flowp. 61
Bernoulli Equation and Potential Flowsp. 63
D'Alembert Paradox and Kutta-Joukowski-Villat Conditionp. 64
More Concerning the K-J-V Conditionp. 67
Potential Flows and Water Wavesp. 73
Formulation of the Water-Wave Problemp. 74
From Cauchy and Poisson to Airy and Stokesp. 75
Boussinesq and KdV Equationsp. 76
Soliton Dynamics, KP, NLS, and NLS-Poisson Equationsp. 77
Compressible Eulerian Baroclinic Fluid Flowp. 82
Lagrangian Invariantsp. 83
Clebsch's and Weber's Transformations. Hamiltonian Form and Cauchy's Integralp. 87
Vector Field Frozen into the Medium and Fridman's Theoremp. 90
A Variational Principlep. 92
The Formation of Vortices and Bjerknes' Theoremp. 94
Various Forms of Euler Equationsp. 96
Isochoric Fluid Flowsp. 101
From Isochoric Fluid Flow to Incompressible Fluid Flowp. 102
Unsteady-State 2-D Casep. 103
Steady-State 2-D Casep. 104
Weakly Nonlinear Long Internal Waves in Stratified Flowsp. 108
Isentropic Fluid Flow and the Steichen Equationp. 110
Isentropic Euler Equationsp. 111
The Steichen Equation for the Velocity Potentialp. 112
Steady Euler Equations and Stream Functionsp. 120
2-D Casep. 121
3-D A diabatic Steady-State Flowsp. 127
Atmospheric Flow Equations and Lee Wavesp. 131
Euler Equations for Atmospheric Motionsp. 131
Generalisation of the Bjerknes' Theorem. Influence of the Coriolis Accelerationp. 133
The Meteorological "Primitive" Kibel Equationsp. 134
The f0-Plane A pproximationp. 134
The Primitive (Kibel) Equationsp. 137
The Quasi-Geostrophic Model Equationp. 141
Adjustment to Geostrophy. Formulation of the Initial Condition for the QG Equation (5.49)p. 143
The Boussinesq Inviscid Equationsp. 146
The Standard Atmospherep. 146
Asymptotic Derivation of Inviscid Boussinesq Equationsp. 148
Steady Boussinesq Casep. 154
From Isochoric Equations to Boussinesq Equationsp. 160
Isochoric Lee Wavesp. 161
Steady-State 2-D Model Problemsp. 161
Isochoric 2-D Steady-State Lee Wavesp. 163
Boussinesq Lee Wavesp. 166
Low Mach Number Flow and Acoustics Equationsp. 171
Euler Incompressible Limit Equationsp. 171
Equation for the Temperature Perturbationp. 173
Equations of Acousticsp. 173
External Aerodynamicsp. 173
Internal Aerodynamicsp. 174
The Singular Nature of the Far Fieldp. 178
Turbo-Machinery Fluid Flowp. 185
Various Facets of an A symptotic Theoryp. 186
Through-Flow Modelp. 189
Flow Analysis at the Leading/Trailing Edges of a Rowp. 193
Complementary Remarksp. 194
A Simple "Two-Stream Function" Approachp. 199
Vortex Sheets and Shock Layer Phenomenap. 203
The Concept of Discontinuityp. 203
Entropy and Vorticity Introduced Behind a Shockp. 204
Jump Relations Associated with a Conservation Lawp. 207
Normal Shockp. 208
Oblique Shockp. 210
The Structure of the Shock Layerp. 215
A Simple Description of the Structure of the Taylor Shock Layerp. 217
Some Properties of the Vortex Sheetp. 221
The Guiraud-Zeytounian "Rolled-Up Vortex Sheet" Theoryp. 224
Rigorous Mathematical Resultsp. 231
Well-Posedness of Eulerian Fluid Flowsp. 232
The Well-Posedness of Eulerian Incompressible Fluid Flowp. 236
The Well-Posedness of Eulerian compressible Fluid Flowp. 242
Solvability of Eulerian Fluid Flowp. 245
The Cauchy-Kowalevski Theoremp. 253
Stability-Instability Conceptp. 258
Existence,Regularity, and Uniquencess Resultsp. 271
Water Waves and Solitary Wavesp. 274
Motion of a Compressible Inviscid Fluidp. 274
The Incompressible Limit of Compressible Euler Equationsp. 276
More Recent Rigorous Resultsp. 277
Referencesp. 281
Indexp. 291
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540414124
ISBN-10: 3540414126
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 295
Published: June 2009
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 1.34