Fluid Dynamics in Astrophysics and Geophysics

Norman R. Lebovitz9780821811207, 0821811207

Table of contents :
Title……Page 1
Lectures in Applied Mathematics – Serie Contents……Page 2
Contents ……Page 6
Preface……Page 7
Historical notes ……Page 8
The nature of the fluid ……Page 9
2. Derivation of equations ……Page 11
Geophysical scaling ……Page 13
3. Fundamental solutions ……Page 15
Steady flow……Page 16
Buoyancy driven flow ……Page 21
Dissipation ……Page 23
Western boundary currents ……Page 26
Slow baroclinic waves ……Page 27
Nonlinearity ……Page 28
Barotropic Rossby waves ……Page 29
Steady planetary flow over a ridge ……Page 32
Steady shear ……Page 35
Shear-oscillatory in time ……Page 37
Shear oscillatory in time and space ……Page 38
Steady strain ……Page 40
Stochastic case ……Page 41
Waves on an adverse current ……Page 44
Expulsion of tracer gradients from a gyre ……Page 45
5. Geostrophic turbulence ……Page 47
Two-dimensional turbulence ……Page 48
Evolution of unforced turbulence ……Page 53
Inertial ranges ……Page 54
References ……Page 61
2. Preliminary considerations ……Page 64
3. Theoretical development ……Page 67
4. The persistence of longwave packets in deep fluids ……Page 73
5. The effect of shear ……Page 75
6. The effect of rotation ……Page 77
7. Two-space-dimensional waves ……Page 78
8. Effect of variable depth ……Page 81
References ……Page 82
2, General formulation and basic assumptions ……Page 84
3. The nonlinear and viscous critical layer regime: R_{cl} = O(1) ……Page 87
3.1. Outer expansion ……Page 88
3.2. Inner expansion ……Page 90
3.3. The amplitude equation ……Page 91
4. The viscous critical layer regime: R_{cl}