Buoyancy Effects in Fluids

Preface......Page 11
1.1 The topics to be discussed......Page 15
1.2 Equilibrium and departures from it......Page 17
1.3 The equations of motion and various approximations......Page 20
1.4 Basic parameters of heterogeneous flows......Page 25
2.1 Waves at a boundary between homogeneous layers......Page 28
2.1.1 Progressive waves in deep water......Page 29
2.1.2 Waves between layers of finite thickness......Page 32
2.1.3 Standing waves......Page 33
2.2 Waves in a continuously stratified fluid......Page 35
2.2.1 Description in terms of modes......Page 36
2.2.2 Description in terms of rays......Page 38
2.2.3 Laboratory experiments on waves in bounded regions......Page 43
2.3.1 Velocity constant with height......Page 45
2.3.2 Lee waves with varying properties in the vertical......Page 48
2.3.3 Reversals of velocity and critical layers......Page 51
2.4.1 The mechanism of resonant interaction......Page 53
2.4.2 Interactionsof interfacial waves......Page 55
2.4.3 Interactions with continuous stratification......Page 58
3.1.1 Interfacial waves......Page 62
3.1.2 Cnoidal and solitary waves......Page 66
3.1.3 Waves and flows in a density gradient......Page 69
3.1.4 Finite amplitude lee waves......Page 72
3.2.1 Steady frictionless flow of a thin layer......Page 78
3.2.2 Internal hydraulic jumps......Page 80
3.2.3 Flow down a slope......Page 82
3.2.4 The \'lock exchange\' problem......Page 84
3.2.5 Gravity currents and noses......Page 86
3.3.1 The problem of selective withdrawal......Page 90
3.3.2 Blocking ahead of an obstacle......Page 93
3.3.3 Upstream wakes and boundary layers......Page 96
3.3.4 Viscous diffusive flows......Page 100
4 INSTABILIY AND THE PRODUCTION OF TURBULENCE......Page 105
4.1.1 The various types of instability......Page 106
4.1.2 The Kelvin-Helmholtz mechanism......Page 108
4.1.3 Interfaces of finite thickness......Page 135
4.1.4 Observations of the breakdown of parallel stratified flows......Page 140
4.2.1 Viscous effects at an interface......Page 145
4.2.2 Thermally stratified plane Poiseuille flow......Page 146
4.2.3 Flows along a sloping boundary......Page 149
4.2.4 Transition to turbulence......Page 152
4.3.1 Classification of the various mechanisms......Page 154
4.3.2 Flows near boundaries......Page 156
4.3.3 Shear instabilities produced by interfacial waves......Page 158
4.3.4 The interaction between wave modes......Page 161
4.3.5 Internal instabilities with continuous stratification......Page 162
5.1 Velocity and density profiles near a horizontal boundary......Page 165
5.1.1 The logarithmic boundary layer......Page 166
5.1.2 The effect of a buoyancy flux......Page 168
5.1.3 Forced and free convection......Page 171
5.1.4 Constant-flux layers in stable stratification......Page 174
5.2 Theories of turbulence in a stratified shear flow......Page 176
5.2.1 Similarity theories of turbulence and diffusion......Page 177
5.2.2 The spectrum of nearly inertial turbulence......Page 178
5.2.3 Arguments based on the governing equations......Page 183
5.3.1 The generation and collapse of turbulent wakes......Page 189
5.3.2 The suppression of turbulence at an interior shear layer......Page 192
5.3.3 Stratified flows in pipes, channels and estuaries......Page 195
5.3.4 Longitudinal mixing and advection......Page 199
6 BUOYANT CONVECTION FROM ISOLATED SOURCES......Page 203
6.1.1 Axisymrnetric turbulent plumes......Page 205
6.1.2 The entrainment assumption......Page 208
6.1.3 Forced plumes......Page 211
6.1.4 Vertical two dimensional plumes......Page 214
6.2.1 A modified entrainment assumption......Page 216
6.2.2 Slowly varying flows......Page 218
6.2.3 Laboratory experiments and their applications......Page 219
6.3.1 Dimensional arguments and laboratory experiments......Page 224
6.3.2 Buoyant vortex rings......Page 227
6.3.3 \'Starting plumes\'......Page 229
6.3.4 Line thermals and bent-over plumes......Page 230
6.4.1 Motions in an unstable environment......Page 232
6.4.2 Plumes in a stable environment......Page 234
6.4.3 Forced plumes and vortex rings in a stable environment......Page 238
6.4.4 Environmental turbulence......Page 241
7 CONVECTION FROM HEATED SURFACES......Page 245
7.1.1 The governing parameters......Page 246
7.1.2 Linear stability theory......Page 248
7.1.3 Finite amplitude convection......Page 249
7.2 Laboratory and numerical experiments on parallel plate convection......Page 253
7.2.1 Observations of laminar convection......Page 254
7.2.2 Measurements at larger Rayleigh numbers......Page 257
7.2.3 Numerical experiments......Page 260
7.3.1 The formation of plumes or thermals near a horizontal boundary......Page 264
7.3.2 The environment as an ensemble of convection elements......Page 268
7.3.3 Convection from small sources in a confined region......Page 269
7.3.4 Penetrative convection......Page 273
7.4 Convection with other shapes of boundary page......Page 277
7.4.1 A heated vertical wall......Page 279
7.4.2 Buoyancy layers at vertical and sloping boundaries......Page 281
7.4.3 Convection in a slot......Page 284
8.1.1 The mechanism of instability......Page 289
8.1.2 Linear stability analysis......Page 291
8.1.3 The form of the convection cell......Page 295
8.1.4 Finite amplitude calculations......Page 297
8.2.1 The \'diffusive\' regime......Page 300
8.2.2 The \'finger\' regime......Page 304
8.2.3 Side boundaries and horizontal gradients......Page 305
8.2.4 Related observations in the ocean......Page 308
8.3 The fluxes across an interface......Page 311
8.3.1 Measurements in the \'diffusive\' regime......Page 312
8.3.2 The time history of several convecting layers......Page 316
8.3.3 Fluxes and structure at a \'finger\' interface......Page 318
8.3.4 The thickness of a \'finger\' interface......Page 321
8.3.5 Convection in a region of variable depth......Page 323
9.1.1 Stirring with oscillating grids......Page 326
9.1.2 Mixing driven by a surface stress......Page 330
9.1.3 The influence of molecular processes......Page 333
9.1.4 Comparison of various methods of stirring......Page 335
9.2.1 The wind-mixed surface layer......Page 337
9.2.2 Seasonal changes of a thermocline......Page 339
9.2.3 Mixing at an atmospheric inversion......Page 344
9.2.4 Other factors limiting the depth of a mixed layer......Page 348
10 INTERNAL MIXING PROCESSES......Page 349
10.1 The observational data......Page 351
10.2 Critical Richardson number criteria......Page 355
10.2.1 Examples of equilibrium conditions......Page 356
10.2.2 Non-equilibrium conditions: step formation......Page 357
10.2.3 Energetics of a layered system......Page 360
10.3.4 Waves and turbulence in large scale flows......Page 362
10.3.1 Mixing at existing interfaces......Page 363
10.3.2 Formation of layers from a smooth gradient......Page 365
10.3.3 Statistical aspects of wave generation and breaking......Page 368
Bibliography and Author Index......Page 376
Recent Publications......Page 396
Subject Index......Page 399