The turbulent ocean

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
Preface......Page 13
Structure and resume......Page 16
Acknowledgements......Page 19
1.1 Introduction......Page 21
1.2 Heat and temperature......Page 23
1.3 Density......Page 25
1.4 Instability and oscillations resulting from buoyancy forces......Page 28
1.5.1 Eulerian and Lagrangian flow descriptions: advection and Stokes drift......Page 32
1.5.2 Molecular conduction......Page 33
1.5.3 Radiation......Page 35
1.5.5 The cold skin of the ocean......Page 36
1.6 Heat capacity of the ocean......Page 37
1.7.1 Shear, convergence and strain......Page 39
1.7.2 Stirring, mixing and entrainment......Page 40
1.7.4 Eddy diffusion of heat, salt and mass......Page 42
1.7.5 The turbulent Reynolds and Prandtl numbers......Page 43
1.7.7 Coherent structures......Page 44
1.7.8 Dissipation: Epsilon, ChiT and ChiS......Page 45
1.7.10 The Batchelor scale......Page 46
1.7.11 The energy spectrum and the first ocean measurements of turbulence......Page 47
1.7.12 The turbulent energy equation......Page 48
1.7.13 The equation for the rate of change of temperature variance......Page 49
1.8.1 Dispersion of neutral particles or floats......Page 50
1.8.2 Richardson’s four-thirds power law......Page 52
1.8.3 Dispersion of passive solutes......Page 53
1.8.5 Turbulence and particles: the Stommel effect......Page 54
1.9 Diapycnal heat transfer in the ocean......Page 57
2.1.1 The mean ocean stratification......Page 64
2.1.2 Internal waves and 'dead water'......Page 65
2.1.3 Internal seiches and solitons......Page 66
2.1.4 The resurgence of interest in the 1960s......Page 67
2.2.1 Small amplitude......Page 70
2.2.2 Finite amplitude effects......Page 71
2.3.1 Wave modes......Page 72
2.3.2 Wave rays......Page 75
2.4 Energy and energy flux......Page 82
2.5 The Garrett–Munk spectrum; the energy in the internal wave field......Page 84
2.6.1 Introduction......Page 87
2.6.2 Elastic scattering......Page 88
2.6.4 Parametric instability......Page 89
2.7.1 Processes at, or near, the sea surface......Page 90
2.7.2 Topography......Page 94
2.7.3 Interior or mid-water processes......Page 96
2.8 Internal waves and vortical mode......Page 97
3.1 Introduction......Page 100
3.2.1 Unstratified flows......Page 103
3.2.2 Two-layer flows......Page 106
3.2.3 General, statically stable, stratification......Page 108
3.2.4 Internal waves in shear flows......Page 109
3.2.5 Analytical solutions in particular cases......Page 110
3.3.1 The formation of billows......Page 112
3.3.2 Billow pairing......Page 117
3.3.4 Convective rolls within billows......Page 119
3.3.5 The onset and 'collapse' of turbulence......Page 122
3.4 Unstratified shear flows......Page 125
3.5 Energy dissipation in stratified flows and the efficiency of mixing......Page 126
3.6 Holmboe instability......Page 129
3.7 The shape of billow patches and the length of billow crests......Page 130
3.8.1 Shear flow......Page 132
3.8.2 Baroclinic and barotropic instability......Page 133
4.1 Introduction......Page 135
4.2.1 Convection in thin layers and the effects of shear......Page 137
4.2.2 Convection in deep layers......Page 139
4.3 Convection near surfaces of uniform buoyancy flux......Page 141
4.4.1 Plumes in unstratified surroundings; the entrainment assumption......Page 143
4.4.2 Plumes in stratified surroundings......Page 144
4.5.1 Hydrothermal plumes......Page 145
4.5.2 Deep convection......Page 148
4.6.1 Instability......Page 151
4.6.2 Layers formed by double diffusion......Page 155
4.6.3 Observations of salt fingers: shadowgraph images and temperature variations......Page 157
4.6.4 Density flux by salt fingers and the cause of layers......Page 159
4.6.5 Intrusive layers: compensating temperature and salinity gradients......Page 160
5.1 Introduction......Page 164
5.2 Static instability or convective overturn......Page 165
5.3 Self-induced shear......Page 166
5.4 The superposition of waves: caustics and standing waves......Page 170
5.5 Resonant interactions and parametric instability......Page 173
5.6.2 An accelerating shear flow......Page 177
5.6.3 Critical level interaction......Page 181
5.6.4 Breaking by convective instability in shear......Page 184
5.8 Breaking of wave groups or wave packets......Page 185
5.9 Three-dimensional breaking......Page 188
5.10 Discussion: mixing processes......Page 189
6.1 Introduction......Page 192
6.2 Instrument platforms and measurement systems......Page 193
6.3.1 The 'direct' method......Page 194
6.3.2 ‘An indirect’ method using the Ozmidov length scale......Page 195
6.3.3 ‘Indirect’ methods using acoustic Doppler......Page 197
6.4 Estimation of ChiT and ChiS......Page 199
6.6 Estimation of KT or KP......Page 200
6.7 Estimates of Gamma......Page 202
6.8 Isotropy......Page 203
6.9 Intermittency and patchiness......Page 205
6.10 Acoustic detection of turbulence......Page 208
7.1 Introduction......Page 210
7.2.4 Intrusions from collapsing regions......Page 212
7.2.5 Layers and vortices in stratified turbulence: vorticity cascade......Page 213
7.3.1 Kelvin--Helmholtz billows......Page 217
7.3.2 The variation of Ri, and the related stratification or mixing......Page 221
7.3.3 Empirical expressions for vertical eddy coefficients......Page 224
7.3.4 Shear and internal waves: semi-empirical expressions for Epsilon......Page 225
7.4 Tracer dispersion experiments in the pycnocline......Page 226
7.5 Diapycnal diffusion in the abyssal ocean......Page 228
7.6 Turbulence from shear and double diffusion......Page 229
7.7 Two-dimensional turbulence......Page 231
8.1 Introduction......Page 233
8.2.1 The viscous sub-layer......Page 235
8.2.3 The outer boundary layer......Page 236
8.2.4 Coherent structures......Page 237
8.2.5 Geothermal heat flux and effects of organic matter......Page 239
8.3.1 Turbulence near the seabed......Page 240
8.3.2 The structure of the benthic mixed layer; benthic fronts......Page 241
8.4 Nepheloid layers......Page 245
9.1 Introduction......Page 248
9.2.1 Types of breaker......Page 251
9.2.2 Laboratory studies and vorticity generation......Page 252
9.2.3 Observations at sea......Page 256
9.2.4 Bubbles and foam......Page 259
9.2.5 Effects of rain on wave breaking......Page 263
9.3.2 The effects of a surface buoyancy flux: severe and prolonged cooling......Page 266
9.3.3 The effects of a surface buoyancy flux: diurnal heating......Page 267
9.4.1 General description......Page 271
9.4.2 Development of the circulation......Page 275
9.5 Temperature ramps......Page 277
9.6.1 Dispersion of dye or neutral solutes......Page 280
9.6.2 Dispersion of floating films or particles......Page 281
9.7.1 Engulfment and entrainment......Page 284
9.7.2 Effects of Langmuir circulation in deepening the mixed layer......Page 285
9.7.4 Internal wave radiation......Page 286
9.8 Turbulence and marine organisms......Page 287
10.1 Introduction......Page 289
10.2.2 Turbulence above the viscous sub-layer: quasi-steady flows over flat topography......Page 290
10.2.3 Flow over rippled beds: form drag and detrainment......Page 291
10.2.4 Turbulence above the viscous sub-layer: oscillatory flows with zero mean flow......Page 296
10.2.5 Turbulence above the viscous sub-layer: oscillatory flows with non-zero mean flow......Page 297
10.3.1 The threshold of sediment motion and sediment erosion......Page 298
10.3.2 Suspended sediment......Page 299
10.3.4 Biological effects on seabed erosion and turbulence......Page 301
10.4.1 Tidal mixing fronts......Page 302
10.4.2 The effect of seabed-generated turbulence on the overlying water......Page 303
10.4.3 Mixing produced by internal waves......Page 306
10.5.1 Shear dispersion in shallow water......Page 307
10.5.3 Dispersion in the thermocline......Page 308
10.6 Regions of horizontal variation in temperature and salinity......Page 310
11.1 Introduction......Page 311
11.2.1 The surf zone......Page 312
11.2.3 Along-shore flows......Page 317
11.3 Shoaling internal waves in the thermocline......Page 319
11.4.1 Wave reflection and critical slopes......Page 323
11.4.2 Resonant interactions......Page 331
11.4.3 Fronts or bores......Page 332
11.4.4 Generation of Eulerian and Lagrangian flows......Page 334
11.5 Along-and upslope circulation......Page 336
11.6 Exchanges between the boundary layer and the interior ocean......Page 337
11.7 Winter cascading and turbidity currents......Page 338
12.2 Headlands, promontories and curved coastlines......Page 341
12.3 Canyons......Page 342
12.4 Isolated topography......Page 343
12.5 Complex rough topography......Page 345
12.6.1 Sea straits: two-layer flows......Page 346
12.6.2 Sea straits: finite interface thickness......Page 350
12.6.3 Sea straits: effects of rotation......Page 351
12.7.1 Sill dynamics......Page 352
12.7.2 Basin response......Page 357
12.8 Lakes......Page 358
13.1 Introduction......Page 360
13.2.1 Distribution......Page 363
13.2.2 The global energy balance......Page 365
13.2.4 Spectra......Page 366
13.3.2 Spirals patterns......Page 368
13.3.3 Filaments......Page 370
13.3.4 Other surface eddies......Page 371
13.3.5 Subsurface eddies: Meddies......Page 372
13.3.7 Pairing of eddies......Page 375
13.4.1 Natural, anthropogenic, and purposeful tracers......Page 377
13.4.2 Surface drifters and sub-surface floats......Page 382
13.5 Rossby waves......Page 385
13.6 Long-term variations......Page 387
14.1 The nature and effects of ocean turbulence......Page 388
14.2 Prediction and unknown energetics......Page 390
14.3 Conclusion......Page 391
1.1 Non-dimensional parameters......Page 393
1.2 Derived dimensional parameters......Page 394
2 Units and symbols......Page 395
4.1 Turbulent dissipation......Page 396
4.5 Internal waves......Page 397
5 Acronyms used in text......Page 398
References......Page 400
Index of laboratory experiments......Page 444
Subject index......Page 446