Stratified Flows

ContentsPreface to Second EditionPreface to First Edition Guides for the Reader 1. Preliminaries 1. General Discussion of the Effects of Density or Entropy Variation 2. The Inertia Effect of Density or Entropy Variation 3. The Gravity Effect of Density or Entropy Variation 4. Creation of Vorticity by Nonhomogeneity 5. The Structure of Stratified Flows Notes 2. Waves of Small Amplitude 1. Introduction 2. The Governing Differential Equations 3. Boundary Conditions 4. Three-Dimensional Waves 5. Effect of Compressibility in an Isothermal Atmosphere 6. The Eigenvalue Problem for the General Case 7. The Eigenvalue Problem for Wave Motion in an Incompressible Fluid 8. Dependence of Phase Velocity on Wavelength for System I 9. Wave Motion in a Bounded Isothermal Atmosphere 10. Wave Motion in an Isothermal Atmosphere with a Free Surface 11. Estimate of Phase Velocity 12. Wave Motion in a Stratified Liquid with Density Discontinuities 13. Propagation of Disturbance in Three Dimensions—Group Velocity 14. Approximate Calculation of Eigenvalues 15. Waves Generated by a Plane Wave Maker 16. Atmosphere Waves in the Lee of Mountains 17. Internal Waves in Basins or Channels of Variable Depth Notes3. Steady Flows of Finite Amplitude 1. Introduction 2. Governing Equation for Two-Dimensional Flows of an Incompressible and Inviscid Fluid 3. Types of Solutions for Steady Flows of an Incompressible Fluid of Variable Density 4. Class I : Pseudopotential Flows 5. Class II : Channel Flows and Large-Amplitude Lee Waves 6. Class II (continued) : Two-Dimensional Stratified Flow into a Sink 7. Class II (continued) : Stratified Flow over a Barrier 8. Class II (continued): The Phenomenon of Blocking 9. Class I I I : Channel Flows and Large-Amplitude Lee Waves with Another Class of Upstream Conditions 10. Compressible Fluids with Variable Entropy 11. Homentropic and Homenergetic Flows over Great Heights 12. Flows with Slight Stratification in Entropy and Specific Energy 13. Axisymmetric Flows 14. Progressive Waves of Permanent Form in Continuously Stratified Fluids 15. Internal Solitary and Cnoidal Waves 16. Steady Flows of a Stratified Fluid in Three Dimensions 17. Shallow-Water Theory for Steady Stratified Flows in Three Dimensions 18. Edge Waves of Finite Amplitude in a Stratified Fluid and Other Results 19. Flows of Homogeneous Layers in a Gravitational Field 20. Internal Hydraulic Jumps 21. Internal Surges 22. Unidirectional Laminar Flows 23. Gravitational Convection from Sources Notes4. Hydrodynamic Stability 1. Introduction 2. Instability of Two Superposed Inviscid Fluids in a Tube 3. Effect of Viscosity on Gravitational Instability 4. Effects of Diffusivities on Gravitational Instability 5. Helmholtz Instability, or Instability of Two Superposed Inviscid Fluids 6. Wave Generation by Wind 7. Stability of Stratified Flows 8. The Dish-Pan Experiments Notes 5. Flows in Porous Media 1. Introduction 2. Steady Two-Dimensional Flows with a Free Surface 3. Velocity of Fluid Masses in Porous Media 4. Steady Flows of a Nonhomogeneous Fluid in Porous Media 5. Stratified Flow in Hele-Shaw Cells 6. Instability Due to a Difference in Viscosity 7. Maintained Gravitational Convection from a Line or Point Source Notes 6. Analogy Between Gravitation and Acceleration 1. Introduction 2. Equations of Motion for an Accelerating System 3. Equations of Motion for a Rotating System 4. Stiffening Effect of Vortex Lines 5. Centrifugal Waves 6. Hydraulic Jump in a Rotating Fluid 7. Large-Amplitude Steady Flows o f a Swirling Fluid 8. Stability of Accelerating Fluids 9. Stability of Rotating Fluids 10. Finite Cavities Attached to Accelerating Bodies Notes 7. Analogy Between Gravitational and Electromagnetic Forces 1. Introduction 2. The Equations Governing Fluid Motion in a Magnetic Field 3. The Stiffening Effect of Magnetic Lines 4. Centripetal Waves 5. Equations Governing Finite-Amplitude Axisymmetric Motion of a Conducting Fluid 6. Simplification of Long's Equation 7. Equations Governing the Motion of an Incompressible Stratified and Conducting Fluid 8. Ring Vortices Generated Electromagnetically Bibliography Index