Waves and mean flows:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | 1. publ. |
| Series: | Cambridge monographs on mechanics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 341 S. |
| ISBN: | 9780521866361 |
Staff View
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| adam_text | Contents
Preface
page
xv
Part I Fluid Dynamics and Waves
1
1
Elements of fluid dynamics
3
1.1
Flow kinematics
3
1.1.1
Mass, momentum and velocity
3
1.1.2
Material trajectories and derivatives
5
1.1.3
Lagrangian and Eulerian variables
6
1.1.4
Evolution of material elements
6
1.2
Perfect fluid dynamics
8
1.2.1
Euler s equation
8
1.2.2
Constitutive relations
9
1.2.3
The polytropic fluid model
10
1.3
Conservation laws and energy
11
1.4
Circulation and vorticity
12
1.4.1
Circulation theorem
12
1.4.2
Vorticity and potential vorticity
14
1.5
Rotating frames of reference
16
1.6
Shallow-water system
18
1.6.1
Available potential energy
19
1.7
Notes on the literature
20
2
Linear waves
21
2.1
Linear dynamics
22
2.1.1
Particle displacements and the virial theorem
23
2.1.2
Vortical and wave modes
24
2.1.3
Kinematics of plane waves
25
2.1.4
Shallow-water plane waves
27
vu
Contents
2.1.5
Refraction
30
2.1.6
WKB theory for slowly varying wavetrains
32
2.1.7
Related wave equations and adiabatic
invariance
36
2.2
Notes on the literature
37
Geometric wave theory
38
3.1
Two-dimensional refraction
39
3.1.1
Characteristics and Fermat s theorem
39
3.1.2
Ocean acoustic tomography
41
3.1.3
Ray tubes
42
3.2
Caustics
44
3.2.1
Green s function representation
44
3.2.2
High-wavenumber boundary-value problem
45
3.2.3
Stationary phase approximation
46
3.2.4
Curved wave fronts and focusing
48
3.2.5
The phase shift across caustics
49
3.2.6
Solution directly on the caustic
50
3.2.7
Non-smooth
wavemakers
and diffraction
51
3.3
Notes on the literature
52
Dispersive waves and ray tracing
53
4.1
Facets of group velocity
53
4.1.1
Beat waves
54
4.1.2
Boundary forcing and radiation condition
54
4.1.3
Asympotic solution to initial-value problem
56
4.1.4
Asymptotic wave energy dynamics
60
4.1.5
The case of equal-and-opposite frequencies
62
4.2
Examples of dispersive waves
64
4.2.1
Rotating shallow water
64
4.2.2
Two-dimensional Rossby waves
67
4.3
Ray tracing for dispersive wavetrains
70
4.3.1
Model example
72
4.3.2
Generic ray-tracing equations
74
4.3.3
Symmetries and ray invariants
76
4.3.4
A note on the asymptotic phase in ray tracing
77
4.4
Ray tracing in moving media
77
4.4.1
Doppler
shifting and the intrinsic frequency
78
4.4.2
Refraction by the basic flow
79
4.4.3
Fermat s principle for dispersive wavetrains
80
4.4.4
Wave action conservation and amplitude
prediction
83
Contents ix
4.5
Wave activity conservation laws
85
4.5.1
Ensemble conservation law in discrete mechanics
86
4.5.2
Ensemble conservation law for linear waves
87
4.5.3
Pseudomomentum and pseudoenergy
88
4.5.4
Wave action for slowly varying wavetrains
90
4.5.5
Moving media and several dimensions
91
4.6
Notes on the literature
93
Part II Wave—Mean Interaction Theory
95
Zonally symmetric wave-mean interaction theory
97
5.1
Basic assumptions
98
5.1.1
Small-amplitude wave-mean interactions
98
5.1.2
Simple geometry
100
5.1.3
Zonal averaging
101
Internal gravity waves
103
6.1
Boussinesq system and stable stratification
103
6.1.1
Momentum, energy and circulation
105
6.2
Linear Boussinesq dynamics
106
6.2.1
Vortical mode
107
6.2.2
Plane internal gravity waves
107
6.2.3
Spatial structure of time-periodic waves
110
6.2.4
Two-dimensional vertical slice model 111
6.3
Zonal pseudomomentum of internal waves 111
6.3.1
Lagrangian and Eulerian pseudomomentum
112
6.3.2
Forcing and dissipation of pseudomomentum
115
6.4
Mountain lee waves and drag force
116
6.4.1
Linear lee waves in two dimensions
117
6.4.2
Hydrostatic solution using Hubert transforms
121
6.4.3
Drag force and momentum flux
122
6.5
Mean-flow response
125
6.5.1
Eulerian-mean equations
125
6.5.2
Mean buoyancy and pressure response
126
6.5.3
Zonal mean-flow response
129
6.5.4
Mass, momentum and energy budgets
130
6.6
Wave dissipation
133
6.6.1
Radiative damping and secular mean-flow
growth
134
6.6.2
Non-acceleration and the pseudomomentum
rule
135
x
Contents
6.7
Extension
to
variable stratification
and density
137
6.7.1
Variable stratification
and wave reflection
138
6.7.2
Density decay and amplitude growth
139
6.8
Notes on the literature
141
7
Shear flows
142
7.1
Linear Boussinesq dynamics with shear
143
7.1.1
Wave activity measures with shear
144
7.1.2
Energy changes for a sheared wavetrain
145
7.1.3
Rayleigh s theorem for shear instability
146
7.1.4
Ray tracing in a shear flow
147
7.2
Critical layers
148
7.2.1
Validity of ray tracing in critical layers
149
7.2.2
Failure of steady linear theory for critical layers
150
7.2.3
Causal linear theory for critical layers
152
7.2.4
Singular wave absorption by dissipation
154
7.2.5
Strongly nonlinear critical layers
156
7.2.6
Numerical simulations and drag parametrization
158
7.2.7
Saturation parametrization of critical layers
158
7.3
Joint evolution of waves and the mean shear flow
160
7.3.1
Multi-scale expansion in wave amplitude
161
7.3.2
Examples of joint wave-mean dynamics
164
7.3.3
The quasi-biennial oscillation
168
7.4
Notes on the literature
170
8
Three-dimensional rotating flow
171
8.1
Rotating Boussinesq equations on an /-plane
171
8.2
Linear structure
172
8.2.1
Balanced vortical mode and Rossby adjustment
172
8.2.2
Internal inertia-gravity waves
175
8.2.3
Rotating lee waves and mountain drag
178
8.3
Mean-flow response and the vortical mode
180
8.3.1
Leading-order response and the
ТЕМ
equations
181
8.3.2
Forcing of mean vortical mode
182
8.4
Rotating vertical slice model
183
8.4.1
Stratification and rotation symmetry
183
8.4.2
Wave-mean interactions in the slice model
184
8.5
Notes on the literature
185
9
Rossby waves and balanced dynamics
186
9.1
Quasi-geostrophic dynamics
186
9.1.1
Governing equations
187
Contents xi
9.1.2
Conservation
properties
189
9.1.3
Quasi-geostrophic /3-plane
191
9.1.4
Response to effective zonal mean force
192
9.2
Small amplitude wave-mean interactions
193
9.2.1
Rossby-wave pseudomomentum
194
9.2.2
Localized forcing and dissipation
194
9.3
Rossby waves and turbulence
196
9.3.1
The Taylor identity for quasi-geostrophic dynamics
196
9.3.2
Turbulent mixing of PV
198
9.3.3
PV staircases and self-sharpening jets
200
9.4
Notes on the literature
203
10
Lagrangian-mean theory
204
10.1
Lagrangian and Eulerian averaging
205
10.1.1
Stokes corrections
207
10.1.2
Stokes drift, pseudomomentum and bolus velocity
209
10.2
Elements of GLM theory
211
10.2.1
Lifting map and Lagrangian averaging
211
10.2.2
The mean material derivative and trajectories
213
10.2.3
Mean mass conservation
214
10.2.4
Small-amplitude relations for the mass density
217
10.2.5
The divergence effect
217
10.2.6
Mean surface elements and conservation laws
220
10.2.7
Circulation and pseudomomentum
223
10.2.8
Why pseudomomentum is conserved
225
10.2.9
Vorticity and potential vorticity
226
10.3
Wave activity conservation in GLM theory
229
10.3.1
General wave activity equation
230
10.3.2
Pseudomomentum and pseudoenergy
232
10.3.3
Non-barotropic flows
234
10.3.4
Angular momentum and pseudomomentum
235
10.4
Coriolis forces in GLM theory
237
10.4.1
Rotating circulation and pseudomomentum
238
10.4.2
Wave activity relations
239
10.4.3
Angular momentum and pseudomomentum
240
10.4.4
Gauged pseudomomentum and the /3-plane
241
10.5
Lagrangian-mean gas dynamics and radiation stress
245
10.5.1
Radiation stress and pseudomomentum flux
246
10.6
Notes on the literature
248
xii
Contents
11
Zonally symmetric GLM theory
249
11.1
GLM theory for the Boussinesq equations
249
11.1.1
Dissipative pseudomomentum rule
252
11.1.2
Pseudomomentum with vertical shear
253
11.2
Rotating Boussinesq equations on an /-plane
254
11.2.1
Residual and Lagrangian-mean circulations
255
11.2.2
EP flux in GLM theory
255
11.2.3
Rotating vertical slice model in GLM theory
256
11.3
Notes on the literature
257
Part III Waves and Vortices
259
12
A framework for local interactions
261
12.1
A geometric singular perturbation
262
12.2
Examples of mean pressure effects
263
12.2.1
Mean-flow response to acoustic wavetrain
264
12.2.2
Mean force on
a
wavemaker
267
12.2.3
Large-scale return flow beneath surface waves
270
12.3
Vortical mean-flow response
274
12.3.1
Local interactions in shallow water
275
12.3.2
Bretherton flow
276
12.3.3
A wavepacket life cycle
278
12.3.4
Strong interactions and potential vorticity
280
12.4
Impulse and pseudomomentum conservation
281
12.4.1
Classical impulse theory
281
12.4.2
Impulse and pseudomomentum in
GLM theory
285
12.5
Notes on the literature
288
13
Wave-driven vortex dynamics on beaches
289
13.1
Wave-driven longshore currents
289
13.2
Classic theory based on simple geometry
291
13.2.1
Wave structure
292
13.2.2
Mean-flow response
294
13.3
Theory for inhomogeneous wavetrains
298
13.4
Vorticity generation by wave breaking and
shock formation
299
13.5
Vortex dynamics on sloping beaches
303
13.5.1
Impulse for one-dimensional topography
304
13.5.2
Self-advection of vortices
305
Contents xiii
13.5.3 Mutual
interaction
of vortices and rip currents
308
13.5.4
A statistical argument for vortex locations
309
13.6
Barred beaches and current dislocation
311
13.6.1
Current dislocation by vortex dynamics
313
13.6.2
Bottom fricton and turbulence
314
13.7
Notes on the literature
315
14
Wave refraction by vortices
317
14.1
Anatomy of wave refraction
318
14.1.1
Refraction by a bath-tub vortex
320
14.2
Remote recoil
321
14.3
Wave capture of internal gravity waves
324
14.3.1
Impulse and pseudomomentum for stratified flow
326
14.3.2
Wavepacket and vortex
dipole
example
329
14.3.3
Mean-flow response at the wavepacket
330
14.4
Wave-vortex duality and dissipation
333
14.5
Notes on the literature
334
References
335
Index
339
|
| any_adam_object | 1 |
| author | Bühler, Oliver |
| author_facet | Bühler, Oliver |
| author_role | aut |
| author_sort | Bühler, Oliver |
| author_variant | o b ob |
| building | Verbundindex |
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| callnumber-subject | QC - Physics |
| classification_rvk | UF 4000 |
| classification_tum | GEO 575f GEO 710f PHY 226f |
| ctrlnum | (OCoLC)299718599 (DE-599)BVBBV035648864 |
| dewey-full | 532/.0593 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.0593 |
| dewey-search | 532/.0593 |
| dewey-sort | 3532 3593 |
| dewey-tens | 530 - Physics |
| discipline | Geowissenschaften Physik |
| edition | 1. publ. |
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| id | DE-604.BV035648864 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:42:25Z |
| institution | BVB |
| isbn | 9780521866361 |
| language | English |
| lccn | 2009012261 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017703504 |
| oclc_num | 299718599 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-634 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-634 DE-91G DE-BY-TUM |
| physical | XIX, 341 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Cambridge monographs on mechanics |
| spelling | Bühler, Oliver Verfasser aut Waves and mean flows Oliver Bühler 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2009 XIX, 341 S. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on mechanics Atmospheric circulation Nonlinear waves Fluid dynamics Wave-motion, Theory of Nichtlineare Welle (DE-588)4042102-8 gnd rswk-swf Wechselwirkung (DE-588)4064937-4 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Welle (DE-588)4065310-9 gnd rswk-swf Allgemeine atmosphärische Zirkulation (DE-588)4202863-2 gnd rswk-swf Geophysik (DE-588)4020252-5 gnd rswk-swf Wellenbewegung (DE-588)4467376-0 gnd rswk-swf Strömung (DE-588)4058076-3 gnd rswk-swf Allgemeine atmosphärische Zirkulation (DE-588)4202863-2 s Nichtlineare Welle (DE-588)4042102-8 s Wellenbewegung (DE-588)4467376-0 s Strömungsmechanik (DE-588)4077970-1 s DE-604 Welle (DE-588)4065310-9 s Wechselwirkung (DE-588)4064937-4 s Strömung (DE-588)4058076-3 s Geophysik (DE-588)4020252-5 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017703504&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bühler, Oliver Waves and mean flows Atmospheric circulation Nonlinear waves Fluid dynamics Wave-motion, Theory of Nichtlineare Welle (DE-588)4042102-8 gnd Wechselwirkung (DE-588)4064937-4 gnd Strömungsmechanik (DE-588)4077970-1 gnd Welle (DE-588)4065310-9 gnd Allgemeine atmosphärische Zirkulation (DE-588)4202863-2 gnd Geophysik (DE-588)4020252-5 gnd Wellenbewegung (DE-588)4467376-0 gnd Strömung (DE-588)4058076-3 gnd |
| subject_GND | (DE-588)4042102-8 (DE-588)4064937-4 (DE-588)4077970-1 (DE-588)4065310-9 (DE-588)4202863-2 (DE-588)4020252-5 (DE-588)4467376-0 (DE-588)4058076-3 |
| title | Waves and mean flows |
| title_auth | Waves and mean flows |
| title_exact_search | Waves and mean flows |
| title_full | Waves and mean flows Oliver Bühler |
| title_fullStr | Waves and mean flows Oliver Bühler |
| title_full_unstemmed | Waves and mean flows Oliver Bühler |
| title_short | Waves and mean flows |
| title_sort | waves and mean flows |
| topic | Atmospheric circulation Nonlinear waves Fluid dynamics Wave-motion, Theory of Nichtlineare Welle (DE-588)4042102-8 gnd Wechselwirkung (DE-588)4064937-4 gnd Strömungsmechanik (DE-588)4077970-1 gnd Welle (DE-588)4065310-9 gnd Allgemeine atmosphärische Zirkulation (DE-588)4202863-2 gnd Geophysik (DE-588)4020252-5 gnd Wellenbewegung (DE-588)4467376-0 gnd Strömung (DE-588)4058076-3 gnd |
| topic_facet | Atmospheric circulation Nonlinear waves Fluid dynamics Wave-motion, Theory of Nichtlineare Welle Wechselwirkung Strömungsmechanik Welle Allgemeine atmosphärische Zirkulation Geophysik Wellenbewegung Strömung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017703504&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT buhleroliver wavesandmeanflows |