Theory and Applications of Nonviscous Fluid Flows

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