Stratified Flows

Stratified Flows is the second edition of the book Dynamics of Nonhomogenous Fluids. This book discusses the flow of a fluid of variable density or entropy in a gravitational field. In this edition, corrections have been made; unnecessary parts have been omitted; and new sections as well as notes on results related to the subject have been added. This book includes a general discussion of the effects of density or entropy and the structure of stratified flows; waves of small amplitude; the Eigenvalue problem; dependence of phase velocity on wavelength; wave motion; steady flows of finite amplitude; and types of solutions for steady flows. This edition also covers other topics such as hydrodynamic stability; flows in porous media; and the analogy between gravitational and electromagnetic forces. This text is recommended for those in the field of physics who would like to be familiarized with stratified flows and its related concepts.

Contents

Preface to Second Edition

Preface 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

Notes

3. 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

Notes

4. 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