Introduction to the Mathematical Theory of Geophysical Fluid Dynamics (eBook)

eBook Download: PDF

1980 | 1. Auflage
271 Seiten
Elsevier Science (Verlag)
978-0-08-087152-3 (ISBN)

Infos

An introduction to the mathematical theory of geophysical fluid dynamics

Inhalt

Front Cover 1
An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics 4
Copyright Page 5
TABLE OF CONTENTS 10
INTRODUCTION 12
CHAPTER 1: EQUATIONS OF MOTION 16
CHAPTER 2: POTENTIAL VORTICITY 22
Problems 26
CHAPTER 3 : NON-DIMENSIONAL PARAMETERS 28
Problems 31
CHAPTER 4: GEOSTROPHIC FLOW 32
Taylor-Proudman Theorem 32
Taylor Column 34
Application to Geophysical Motion 37
ß- Plane Approximation 39
Problems 44
CHAPTER 5: THE EKMAN LAYER 46
Ekman Layer Equations 50
Example of Cylindrical Flow 54
Ekman Layer Spiral 57
Mass Transport in the Ekman Layer 58
Spin-up Time Scale 59
Tea-cup Experiment 63
Problems 65
CHAPTER 6: THE GEOSTROPHIC MODES 68
The Geostrophic Mode in a Sphere 69
Geostrophically Free, Guided, and Blocked Regions 73
Circulation 74
Problems 76
CHAPTER 7: INERTIAL MODES 78
. Real and |.|< 2
Orthogonality 81
Mean Circulation Theorem 82
Initial Value Problem 83
Inertial Modes in a Cylinder 85
Plane Wave Solution 88
Problems 91
CHAPTER 8: ROSSBY WAVES 96
Sliced Cylinder 97
ß-Plane Problem 100
Plane Wave Solution 106
Problems 108
CHAPTER 9: VERTICAL SHEAR LAYERS 110
E1/3- Layer 111
E1/4-Layer 113
Sliced Cylinder 121
An Ocean Model: Sverdrup’s Relation 125
Problems 131
CHAPTER 10: ANALOGIES BETWEEN ROTATION AND STRATIFICATION 134
Problems 142
CHAPTER 11: THE NORMAL MODE PROBLEM FOR ROTATING STRATIFIED FLOW 144
The Steady Flow 148
Potential Vorticity 152
Problems 158
CHAPTER 12: ROSSBY WAVES IN A ROTATING STRATIFIED FLUID 162
The Potential Vorticity Equation 162
Rossby Waves for a Stratified Fluid 164
Rossby Radius of Deformation 167
Problems 170
CHAPTER 13: INTERNAL WAVES IN A ROTATING STRATIFIED FLUID 172
Plane Wave Solution 174
Waves in Bounded Geometry 177
Variable N( z ) 187
Oceanographic Results 198
Problems 200
CHAPTER 14: BOUNDARY LAYERS IN A ROTATING STRATIFIED FLUID 202
The Stratified Ekman Layer 204
The Side-wall Layers 207
Problems 217
CHAPTER 15: SPIN-DOWN IN A ROTATING STRATIFIED FLUID 220
Spin-down in a Cylinder 223
Secular Growth 230
The Steady Solution 231
The Decaying Modes 233
Further Comments 237
Problems 239
CHAPTER 16: BAROCLINIC INSTABILITY 242
The Eady Model 243
The Stability Criterion 247
Experiments: Laboratory Models 254
Problems 258
APPENDIX BOUNDARY LAYER METHODS 260
BIBLIOGRAPHY 274
INDEX 280

Produkt-Details

• Erscheint lt. Verlag: 1.1.1980
• Mitarbeit: Herausgeber (Serie): Susan Friedlander
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 0-08-087152-6 / 0080871526
• ISBN-13: 978-0-08-087152-3 / 9780080871523