Hydrodynamics of Oceans and Atmospheres
Free Global Shipping
No minimum orderDescription
Hydrodynamics of Oceans and Atmospheres is a systematic account of the hydrodynamics of oceans and atmospheres. Topics covered range from the thermodynamic functions of an ideal gas and the thermodynamic coefficients for water to steady motions, the isothermal atmosphere, the thermocline, and the thermosphere. Perturbation equations, field equations, residual equations, and a general theory of rays are also presented. This book is comprised of 17 chapters and begins with an introduction to the basic equations and their solutions, with the aim of illustrating the laws of dynamics. The nonlinear equations of thermodynamics and hydrodynamics are analyzed using the methods of perturbation theory, with emphasis on the zero-order solution; zero-order states of an ideal gas; the first-order equations; the additive barotropic terms; and boundary conditions. The following chapters focus on the steady component of atmospheric pressure; free steady motion with or without rotation; field equations and general theorems relating to such equations; and the stratification of the Earth's atmosphere, oceans, and lakes. The next two chapters present calculations concerning the isothermal atmosphere, with particular reference to plane level surfaces with or without rotation. The final chapter looks at spherical level surfaces with rotation. This monograph will be of interest to physicists, oceanographers, atmospheric scientists, and meteorologists.
Table of Contents
Preface
Chapter I. The Basic Equations
1. Introduction
2. Thermodynamics
3. The Thermodynamic Functions of an Ideal Gas
4. The Thermodynamic Coefficients for Water
5. Hydrodynamics
Gravitational Potential
Rotation
Forces
Accession of Heat, Advection
Elimination of Entropy
Conservation of Energy
Chapter II. The Perturbation Equations
6. Introduction
7. The Zero-Order Solution
Barotropic States
The Gradients
8. Zero-Order States of an Ideal Gas
The Isothermal Atmosphere
The Isentropic Atmosphere
Atmosphere with Constant Temperature Gradient
General Case
9. The First-Order Equations
Interpretations
Vertical Displacement
10. The Additive Barotropic Terms
11. Boundary Conditions
Chapter III. Steady Motions
12. Introduction
Mean Pressure
The Zonal Component
The Tesseral Component
The Oceans
The Atmosphere and Oceans as a Heat Engine
The Equations
13. Free Steady Motion, No Rotation
Plane Level Surfaces
Spherical Level Surfaces
14. Second-Order Instability; The Secular Equation
Secular Equations
Relation to the Vorticity Theorem
A First Integral of the Secular Equation
Relation to the Bernoulli Theorem
15. Free Steady Motion with Rotation
The Geostrophic Equation
Relation between Density and Pressure
Planetary Vorticity
Plane Level Surfaces
Spherical Level Surfaces
16. Pure Convection, No Rotation
The Vertical Velocity
Boundary Conditions
Consequences of the Conservation of Matter
Explicit Solution of the Equations
Plane Level Surfaces
Spherical Level Surfaces
17. Pure Convection, with Rotation
Thermobaric Motion
Density and Pressure
Plane Level Surfaces
Spherical Level Surfaces
18. Hadley's Hypothesis of Zonal Heating
No Rotation
Instability of the Hadley Vortices
19. Analysis of the Earth's Permanent Pressure Field
The Zonal Component of Pressure
The Tesseral Component of pressure
The Effects of Terrain
Chapter IV. The Field Equations
20. Introduction
21. The External and Thermobaric Energies
22. The Field Variables
Oceanic Case
Isothermal Atmosphere
Atmosphere with Constant Temperature Gradient
23. The Field Equations
24. Significance of the Coefficients N and T
25. Special Formula for the Coefficients
Perfect Gas
Fresh Water
Sea-water
Chapter V. The Earth's Atmosphere, Oceans and Lakes
26. Introduction
27. The Stratification of the Oceans
Large-scale Averages
Small-scale Averages
28. The Stratification of Freshwater Lakes
29. The Stratification of the Earth's Atmosphere
30. Planetary Rotation and Cyclogenesis
Early Ideas
Observations of Redfield and Reid: Cyclones
Tracy's Theory
Hann's Theory
Cyclones and Anticyclones
Vorticity
Helmholtz and Bjerknes Vorticity Theorems
31. First-Order Cyclogenesis
No Rotation
Rotation
Rotation with Spherical Level Surfaces
Summary
Chapter VI. General Theorems concerning the Field Equations
32. Introduction
33. The Eigensolutions
34. The Expansion Theorem
Expansion Theorem (for a Finite Volume)
Expansion Theorem (for an Infinite Volume)
Chapter VII. Formulation of the Major Mathematical Problems
35. Introduction
36. The Case of no Rotation
Plane Level Surfaces
Residual Equations
Separation of Variables: The Two-dimensional Wave Equation
Spherical Level Surfaces
Residual Equations
Separation of Variables
Wave Equation for a Spherical Surface
37. Rotation with Plane Level Surfaces
The Traditional Approximations
Separation of Variables
Two-Dimensional Wave Equation
Calculation without the Approximation
Separation of Variables
38. Rotation with Spherical Level Surfaces
The Traditional Approximation
Separation of Variables: Laplace's Tidal Equation
Omission of the Traditional Approximations
39. Complex Vectors and the Hodograph
No Rotation
Rotation: Traditional Approximation
Rotation: Without Approximation
Chapter VIII. The Isothermal Atmosphere: Plane Level Surfaces without Rotation
40. Introduction
41. Lamb's Waves
42. Other Eigensolutions; Simple Waves
43. The Propagation Surface; Phase Velocity
44. Rays and Group Velocity
45. The Pressure-Entropy Impedance
46. The Flow and Partition of Energy in Simple Waves
47. The Eigensolutions
The Phase Diagram
The Hodograph
48. The Gravity Waves and the Fluctuating Wind
Chapter IX. The Isothermal Atmosphere: Plane Level Surfaces with Rotation
49. Vertical Axis of Rotation
50. Lamb's Waves
51. Simple Waves and Eigensolutions
52. Sub-Critical Stability
53. Inclined Axis of Rotation
Lamb's Waves
The Laws of Reflection
Conclusions
Chapter X. Oceans with Constant Coefficients
54. Introduction
55. Theory of an Homogeneous Compressible Ocean
56. Theory of a Stratified but Incompressible Ocean
57. The General Case
58. A Simple Approximation for the Internal Gravity Modes
59. The Modes of a Rectangular Tank
60. Other Lateral Boundaries
Chapter XI. General Theory of Rays
61. Introduction
62. The Hamilton-Jacobi Equation
63. Plane Level Surfaces: Vertical Axis
General and Complete Solutions
The Hamilton-Jacobi Function
64. The Rays and Group Velocity
Derivation of the Rays
The Group Velocity
Interpretation of the Ray-Point
Explicit Equations for the Rays
General Properties of the Rays
Limiting Forms of the Rays
65. Spherical Level Surfaces: no Rotation
The Complete Solution
The Rays; The Rays are Plane Curves
Altitude of the Rays
66. Spherical Level Surfaces with Rotation: Traditional Approximation
The Tracks of the Rays
Concerning the Approximation
The Period of the Ray Tracks
Altitude of the Rays
Chapter XII. The Thermocline
67. Formulation of the Problem
68. Preliminary Discussion of the Rays
69. The Sound Waves of Area II
70. The Gravity Waves of Area III
71. The Waves of Areas IV and V
72. The Residual Equations
Modification When the Thermocline Channel Extends to Surface or Bottom
73. Analytic Solution of the Residual Equations
74. Further Application of the W-K-B- Approximation
The Acoustic Modes of Area II
The Internal Gravity Modes of Area III
75. The Two-Layer Model
Chapter XIII. The Thermosphere
76. Introduction
77. The Case of no Rotation
Formal Calculation of the Rays
Interpretation of the Results
78. Vertical Axis of Rotation
79. Solution of the Residual Equations
80. The W-K-B Approximation
Chapter XIV. General Theory of the Residual Equations
81. Introduction
82. Canonic Form of the Residual Equations
The Canonic Variables
The Canonic Equations
Constant Coefficients
The Phase Diagram
83. General Theorems concerning the Phase Paths
84. Sturm's Comparison Theorem
Sturm's Formula
The Oscillation Theorems
Dependence on the Parameters
85. The W-K-B Approximation
Chapter XV. Applications of the General Theory
86. The Thermosphere
87. The Modal Curves and the Comparison Theorem
88. An Atmosphere with a Single Temperature Minimum
89. The Modal Equation for an Ocean of Constant Depth
Chapter XVI. The Wave Equation for a Spherical Surface
90. Introduction
91. The Legendre Functions
Separation of Variables
The Legendre Equation
The Legendre functions
Expressions for the Velocities
Natural Boundary Conditions
The Phase Diagrams
92. Segmental Ocean
Chapter XVII. Spherical Level Surfaces with Rotation
93. Introduction
94. The First-Order Tidal Equations
95. The Zonal Oscillations
Connection with Spheroidal Wave Functions
The Functions Sml(h,τ)
The Phase Paths
96. The Solutions near the Poles
97. The Tidal Equations in Canonic Form
The Signatures
The Phase Paths
The Modal Curves
Transformation to the (χ, ω) Plane
98. The High-Frequency Limit
99. The Semi-Diurnal Oscillations
100. Oscillations of the Second Kind, and the "Long Waves"
The Eigensolutions
The Phase Paths
Positive Speed
The Rossby Waves
Appendix: Mercator Co-ordinates
Index
Product details
- No. of pages: 302
- Language: English
- Copyright: © Pergamon 1960
- Published: January 1, 1960
- Imprint: Pergamon
- eBook ISBN: 9781483149561
About the Author
Carl Eckart
Ratings and Reviews
There are currently no reviews for "Hydrodynamics of Oceans and Atmospheres"