In his book, John Green presents a unique personal insight into the fundamentals of fluid mechanics and atmospheric dynamics. Generations of students have benefited from his lectures, and this book, many years in the making, is the result of his wide teaching and research experience. The theory of fluid flow has developed to such an extent that very complex mathematics and models are currently used to describe it, but many of the fundamental results follow from relatively simple considerations: these classic principles are derived here in a novel, distinctive, and at times even idiosyncratic, way. The book is an introduction to fluid mechanics in the atmosphere for students and researchers that are already familiar with the subject, but who wish to extend their knowledge and philosophy beyond the currently popular development of conventional undergraduate instruction.
Author(s): John Green
Series: Cambridge Atmospheric and Space Science Series
Publisher: Cambridge University Press
Year: 2004
Language: English
Pages: 223
Contents......Page 5
Introduction......Page 11
1.1 Introduction......Page 13
1.2 Spectrum of motion......Page 14
1.3 How isolated phenomena appear in wavenumber-space......Page 17
1.4 Repeated phenomena......Page 19
1.5 Contribution of phenomena to the global kinetic energy spectrum......Page 20
1.6 What do we learn?......Page 21
1.7 Good and bad descriptions of phenomena......Page 22
2.2 The substantial derivative......Page 28
2.4 Remaining confusion......Page 30
2.5 The hydrostatic equation......Page 31
2.6 Pressure as vertical coordinate......Page 32
2.7 Other coordinates......Page 34
2.8 General transformation of coordinates......Page 35
3.1 Momentum......Page 36
3.2 Rotating axes......Page 38
3.3 Motion independent of longitude......Page 39
3.4 Continuity of mass......Page 41
3.5 Continuity of energy......Page 42
3.6 Dry adiabatic......Page 43
3.7 Wet adiabatic......Page 44
3.8 Thermodynamic processes......Page 45
3.9 Energetics......Page 46
3.10 Completeness......Page 47
3.11 Vorticity......Page 48
3.12 The terms in the vorticity equation......Page 49
3.13 Circulation......Page 50
3.14 The shallow atmosphere......Page 51
3.15 Some other forms of the vorticity equation......Page 52
4.1 Nature of approximation......Page 54
4.2 Nearly horizontal atmosphere analysed......Page 55
4.3 The linearised equations......Page 56
4.4 Boundary conditions......Page 60
4.5 Application to the real atmosphere......Page 61
4.7 Simplified solutions......Page 63
4.8 Elastic waves eliminated......Page 64
4.9 Compressible-Boussinesq......Page 65
4.10 Hydrostatic approximation alone......Page 66
4.11 Quasi-geostrophic motion and Rossby waves......Page 67
5.1 More realistic gravity waves......Page 73
5.2 Adiabatic perturbation of steady flow......Page 74
5.3 Refraction and reflection......Page 75
5.4 Propagation of energy......Page 77
5.5 Gravity waves generated by stationary flow over an obstacle......Page 79
5.6 Gravity waves generated by an isolated obstacle......Page 82
5.7 Trapped waves (lids lead to resonance)......Page 84
6.1 Helmholtz instability......Page 86
6.2 Helmholtz waves of finite amplitude......Page 88
6.3 Short waves and viscosity......Page 92
6.4 Short waves; distributed shear......Page 93
6.5 Short waves and stratification......Page 95
6.6 Energetics of sheared stratified overturning......Page 96
6.8 Stratification outside the shear zone......Page 97
6.9 Shear with gravitationally unstable stratification......Page 100
6.10 Turbulence near the ground......Page 101
7.1 Hydrostatics......Page 103
7.2 Effect of molecular diffusivity......Page 104
7.4 Convection in shear......Page 107
7.5 A possible linear selection process......Page 108
7.6 Steady convective overturning......Page 109
7.7 Updraught slope......Page 111
7.8 Real convection......Page 112
8.1 Definition of mesoscale......Page 114
8.2 Above the logarithmic layer......Page 115
8.3 The Taylor-Ekman layer......Page 116
8.4 Communication with the free atmosphere......Page 117
8.6 The cold slab......Page 119
8.7 Slow disturbance about a state of no motion......Page 121
8.8 Continually balanced motion......Page 123
8.9 Evolution of the mean flow......Page 124
8.10 More general forcing......Page 125
9.2 Scale analysis......Page 127
9.3 Simplified equations......Page 129
9.4 Potential vorticity......Page 131
9.5 The parcel theory of baroclinic instability......Page 132
9.6 Simplest baroclinic wave......Page 133
9.8 The slantwise nature of the convection......Page 136
9.9 More general stability problems......Page 137
9.10 Short waves......Page 138
9.11 Integral constraints......Page 141
9.12 Another integral relation......Page 142
9.13 Completeness and the complex plane......Page 143
10.1 Perturbations of inconstant shape: the missing baroclinic wave......Page 144
10.2 A complete set of solutions......Page 146
10.3 A complete solution......Page 147
10.4 Rate of amplification of the inconstant wave......Page 149
10.5 General baroclinic waves with two lids......Page 150
10.6 Predictability......Page 152
11.1 The barotropic quasi-geostrophic vorticity equation......Page 154
11.3 Lids lead to resonance......Page 155
11.4 Surface friction......Page 156
11.6 Very deep atmosphere......Page 157
11.7 Upward propagation of energy......Page 158
11.8 Propagation in the real atmosphere......Page 161
11.9 Lateral dispersion......Page 162
11.10 Longitudinal horizontal dispersion......Page 163
11.12 Dispersion and dissipation......Page 167
12.2 Simulation......Page 169
12.3 Academic modelling......Page 170
12.5 Ice-albedo feedback......Page 171
12.6 Two-dimensional ice-albedo feedback......Page 173
12.8 Physics and numerical gridpoint models......Page 175
12.9 Linear computational instability......Page 177
12.10 Non-linear computational instability......Page 179
13.2 Models with two levels......Page 182
13.3 Two layers......Page 186
13.4 Two parameters......Page 188
13.6 Spectral models......Page 189
13.7 A simple spectral model......Page 190
13.8 Some non-linear solutions......Page 192
13.9 Non-linear baroclinic wave with friction......Page 194
13.10 What do we learn from such exercises?......Page 195
14.1 Transfer......Page 196
14.2 Mixing......Page 197
14.3 Unresolved transport is not always mixing......Page 198
14.4 Transfer of energy......Page 199
14.5 Transfer of momentum......Page 201
14.7 Diffusion and shear......Page 202
14.8 Diffusion and deformation......Page 204
15.1 Definition of general circulation......Page 206
15.2 Zonal mean observed......Page 207
15.3 Zonal mean dissected; thermodynamics......Page 208
15.4 Zonal mean dissected; zonal component of momentum......Page 210
15.5 Zonal mean dissected; meridional component of momentum......Page 211
15.6 Horizontal transfer of momentum......Page 212
15.7 A model of the general circulation; parameterisation......Page 213
15.8 Some simple models of the general circulation......Page 215
15.9 Stationary waves......Page 217
15.10 More general transfer......Page 218
Appendix......Page 221
Index......Page 222
