Internal gravity waves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 357 - 366 |
| Beschreibung: | XV, 377 S. Ill, graph. Darst. 25 cm |
| ISBN: | 9780521839150 0521839157 |
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| 100 | 1 | |a Sutherland, Bruce R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Internal gravity waves |c B. R. Sutherland |
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2010 | |
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Datensatz im Suchindex
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| adam_text | Titel: Internal gravity waves
Autor: Sutherland, Bruce R
Jahr: 2010
Contents
Preface page xiii
1 Stratified fluids and waves 1
1.1 Introduction 1
1.2 Stratified fluids 1
1.2.1 Stratified liquids and the ocean 2
1.2.2 Stratified gases and the atmosphere 4
1.3 Internal gravity waves 6
1.4 Co-ordinate systems 7
1.5 Lagrangian and Eulerian frames of reference 8
1.6 Equations of state 11
1.6.1 Equations of state for air 11
1.6.2 Equations of state for sea water 12
1.7 Conservation of internal energy 13
1.7.1 Thermodynamics of dry air 13
1.7.2 Potential temperature of a gas 15
1.7.3 Thermodynamics of sea water 18
1.8 Conservation of mass 19
1.9 Incompressibility 21
1.10 Conservation of momentum 23
1.10.1 The buoyancy force 24
1.10.2 The pressure gradient force 25
1.10.3 The Coriolis force 25
1.10.4 The viscous damping force 29
1.11 Hydrostatic balance 30
1.12 The Boussinesq and anelastic approximations 33
1.12.1 The speed of sound 34
1.12.2 Boussinesq liquids 34
1.12.3 Non-Boussinesq liquids 38
Contents
1.12.4 Anelastic gases 39
1.12.5 Boussinesq gases 41
1.13 Conservation of angular momentum 43
1.13.1 Vorticity in uniform-density fluid 43
1.13.2 Vorticity in stratified fluid 45
1.13.3 Potential vorticity 46
1.14 Conservation of mechanical energy 48
1.14.1 Kinetic and potential energy 48
1.14.2 Available potential energy 50
1.14.3 The Bernoulli equation 51
1.15 Wave theory 52
1.15.1 Representation of plane waves 53
1.15.2 The dispersion relation 56
1.15.3 Phase velocity 56
1.15.4 Group velocity 58
1.15.5 Representation of wavepackets 60
1.15.6 Plane wave and wavepacket evolution equations 62
1.15.7 Wave modes 65
1.15.8 Cross-correlations 66
Interfacial waves 74
2.1 Introduction 74
2.2 Surface waves 75
2.2.1 Finite-amplitude equations 75
2.2.2 Small-amplitude approximation 77
2.2.3 Dispersion relation, phase and group speeds 79
2.2.4 Polarization relations 80
2.2.5 Fluid parcel motion 84
2.2.6 Energy transport 84
2.2.7 Momentum deposition 88
2.2.8 The Stokes drift 90
2.2.9 Momentum transport 92
2.2.10 Shallow water equations 96
2.3 Interfacial waves in a two-layer fluid 97
2.3.1 Equations of motion 98
2.3.2 Interfacial waves in infinite-depth fluid 100
2.3.3 Interfacial waves in finite-depth fluid 102
2.3.4 Shallow interfacial waves 104
Contents ix
2.4 Interfacial waves in multi-layer fluids 107
2.5 Laterally bounded interfacial waves 112
2.6 Shear flows 115
2.6.1 Derivation of equations 115
2.6.2 Rayleigh waves 118
2.6.3 Shear layer instability in uniform-density fluid 120
2.6.4 Shear instability of interfacial waves 122
2.7 Interfacial waves influenced by rotation 129
2.7.1 Small-amplitude wave equations 131
2.7.2 Inertial waves 132
2.7.3 Energetics of inertial waves 135
Internal waves in uniformly stratified fluid 141
3.1 Introduction 141
3.2 The buoyancy frequency 141
3.2.1 Vertical oscillations of a liquid 142
3.2.2 Vertical oscillations of an ideal gas 144
3.2.3 Stable, neutral and uniform stratification 148
3.2.4 Diagonal oscillations of a liquid 149
3.3 Boussinesq internal waves 151
3.3.1 Equations of motion in a liquid 151
3.3.2 Equations of motion in a Boussinesq gas 153
3.3.3 Dispersion relation 155
3.3.4 Phase and group velocity 157
3.3.5 Polarization relations 159
3.3.6 Hydrostatic and nonhydrostatic waves 161
3.3.7 Evanescent disturbances 163
3.4 Transport by Boussinesq internal waves 164
3.4.1 Zero mass/internal energy transport 165
3.4.2 Mechanical energy transport 166
3.4.3 Wave action and pseudoenergy 170
3.4.4 Momentum transport 172
3.4.5 Wave-induced mean flow 173
3.5 Bounded internal waves 177
3.5.1 Modes in rectangular box 178
3.5.2 Modes in non-uniform stratification 179
3.5.3 Internal waves near slopes 182
3.6 Non-uniformly stratified shear flows 184
3.6.1 Equations of motion 184
3.6.2 Singularities 186
3.6.3 Stability criteria 188
Contents
3.6.4 Piecewise-linear theory 189
3.6.5 Waves in uniform flow with uniform stratification 191
3.6.6 Trapped internal gravity waves 191
3.6.7 Shear instability in stratified fluid 194
3.7 Non-Boussinesq internal waves 197
3.7.1 Non-Boussinesq waves in a liquid 197
3.7.2 Anelastic waves in a gas 201
3.8 Internal waves influenced by rotation 206
Nonlinear considerations 213
4.1 Introduction 213
4.2 Weakly nonlinear theory 213
4.2.1 The nonlinear pendulum 214
4.2.2 Weakly nonlinear theory for partial differential equations 216
4.2.3 The nonlinear Schrödinger equation 218
4.2.4 Modulational stability theory 220
4.3 Weakly nonlinear interfacial waves 222
4.3.1 Theory for interfacial waves in infinitely deep fluid 222
4.3.2 Deep water waves 226
4.3.3 Deep interfacial plane waves 228
4.3.4 Deep interfacial wavepackets 229
4.3.5 Interfacial waves in finite-depth fluid 230
4.4 Solitary waves 232
4.4.1 Nonlinear shallow water equations 233
4.4.2 Moderately long weakly nonlinear interfacial waves 237
4.5 Weakly nonlinear internal waves 240
4.5.1 Perturbation theory 241
4.5.2 Modulational stability 244
4.6 Breakdown of internal waves into turbulence 248
4.6.1 Parametric subharmonic instability 248
4.6.2 Overturning instabilities 253
4.6.3 Shear instabilities 254
4.6.4 Overturning driven by self-acceleration 257
Generation mechanisms 262
5.1 Introduction 262
5.2 Oscillating bodies 262
5.2.1 Oscillating cylinder in inviscid fluid 263
5.2.2 Oscillating cylinder in viscous fluid 270
5.2.3 Oscillating sphere 274
5.3 One-and two-layer flow over topography 281
5.3.1 Equations of motion for a one-layer fluid 281
Contents xi
5.3.2 One-layer small-amplitude hydrostatic flow 282
5.3.3 One-layer small-amplitude nonhydrostatic flow 285
5.3.4 Two-layer flow 287
5.4 Steady stratified flow over topography 290
5.4.1 Froude and long numbers 290
5.4.2 Flow over small-amplitude periodic hills 291
5.4.3 Internal waves over small-amplitude localized hills 299
5.4.4 Internal waves over large-amplitude localized hills 301
5.4.5 Internal waves over localized two-dimensional hills 305
5.4.6 Downslope windstorms 306
5.5 Tidal flow over topography 309
5.5.1 Barotropic tides 309
5.5.2 Inertia gravity wave beams 310
Wave propagation and spectra 315
6.1 Introduction 315
6.2 Extrinsic and intrinsic frequencies 316
6.3 Ray theory 317
6.3.1 General theory 317
6.3.2 Ray theory for waves in two dimensions 320
6.4 Ray theory for interfacial waves 321
6.4.1 Surface waves approaching a beach 321
6.4.2 Interfacial waves approaching a slope 324
6.5 Ray theory for internal waves 326
6.5.1 Internal waves in two dimensions 326
6.5.2 Critical levels 328
6.5.3 Reflection levels 333
6.5.4 Caustics 336
6.6 Eckart resonance and tunnelling 338
6.6.1 Eckart resonance 339
6.6.2 Transmission and reflection of incident plane waves 342
6.7 Internal wave spectra 346
6.7.1 Oceanic internal waves 347
6.7.2 Atmospheric internal waves 352
Suggestions for further reading 357
A.l Textbooks 357
A.2 Review articles 357
A.3 Journal articles 358
A.3.1 Anelastic and other non-Boussinesq equations 358
A.3.2 Momentum and energy transport 358
A.3.3 Stratified shear flow stability 359
xii Contents
A3 A Internal waves at sloping boundaries and attractors 359
A.3.5 Evolution of finite-amplitude internal gravity waves 359
A.3.6 Evolution of internal solitary waves 360
A.3.7 Parametric subharmonic instability of internal
gravity waves 360
A.3.8 Internal wave interaction with its induced mean flow 361
A.3.9 Interaction between internal wave beams 361
A.3.10 Internal wave breakdown 361
A.3.11 Internal wave generation by oscillating bodies 361
A.3.12 Internal wave generation by steady flow over
topography 362
A.3.13 Internal solitary wave generation by flow over
topography 362
A.3.14 Inertia gravity wave generation by tidal flow 363
A.3.15 Internal waves at critical and reflection levels 363
A.3.16 Internal wave ducting and tunnelling 364
A.3.17 Internal waves in transient and veering flows 364
A.3.18 Oceanic internal wave spectra 365
A.3.19 Atmospheric internal wave spectra 365
A.3.20 Drag parameterization in general circulation models 366
Index 367
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:40:38Z |
| institution | BVB |
| isbn | 9780521839150 0521839157 |
| language | English |
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| physical | XV, 377 S. Ill, graph. Darst. 25 cm |
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| publisher | Cambridge Univ. Press |
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| spelling | Sutherland, Bruce R. Verfasser aut Internal gravity waves B. R. Sutherland Cambridge [u.a.] Cambridge Univ. Press 2010 XV, 377 S. Ill, graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 357 - 366 Gravitationswelle (DE-588)4158119-2 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Gravitationswelle (DE-588)4158119-2 s Strömungsmechanik (DE-588)4077970-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026121400&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sutherland, Bruce R. Internal gravity waves Gravitationswelle (DE-588)4158119-2 gnd Strömungsmechanik (DE-588)4077970-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4158119-2 (DE-588)4077970-1 (DE-588)4114528-8 |
| title | Internal gravity waves |
| title_auth | Internal gravity waves |
| title_exact_search | Internal gravity waves |
| title_full | Internal gravity waves B. R. Sutherland |
| title_fullStr | Internal gravity waves B. R. Sutherland |
| title_full_unstemmed | Internal gravity waves B. R. Sutherland |
| title_short | Internal gravity waves |
| title_sort | internal gravity waves |
| topic | Gravitationswelle (DE-588)4158119-2 gnd Strömungsmechanik (DE-588)4077970-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Gravitationswelle Strömungsmechanik Mathematisches Modell |
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