A modern introduction to the mathematical theory of water waves:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge texts in applied mathematics
19 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008116284&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XIV, 445 S. graph. Darst. |
| ISBN: | 0521591724 052159832X |
Internformat
MARC
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| 100 | 1 | |a Johnson, R. S. |d 1944- |e Verfasser |0 (DE-588)122078942 |4 aut | |
| 245 | 1 | 0 | |a A modern introduction to the mathematical theory of water waves |c R. S. Johnson |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1997 | |
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Datensatz im Suchindex
| _version_ | 1819269243221311488 |
|---|---|
| adam_text | Contents
, page xi
atical preliminaries 1
eraing equations of fluid mechanics 2
ie equation of mass conservation 3
:e equation of motion: Euler’s equation 5
^orticity, streamlines and irrotational flow 9
ijiridary conditions for water waves 13
ie kinematic condition 14
ie dynamic condition 15
fjTie bottom condition 18
integrated mass conservation condition 19
energy equation and its integral 20
önsionalisation and scaling 24
ondimensionalisation 24
ding of the variables 28
Ipproximate equations 29
ents of wave propagation and asymptotic expansions 31
ementary ideas in the theory of wave propagation 31
symptotic expansions 35
reading 46
47
ical problems in water-wave theory
61
oblems
opagation for arbitrary depth and wavelength
irticle paths
62
62
67
viii
2 2
2 3
2 4
II
2 5
2 6
2 7
2 8
2 9
3
3 1
3 2
Contents
212 Group velocity and the propagation of energy
213 Concentric waves on deep water
Wave propagation over variable depth
221 Linearised gravity waves of any wave number moving
over a constant slope
222 Edge waves over a constant slope
Ray theory for a slowly varying environment
231 Steady, oblique plane waves over variable depth
232 Ray theory in cylindrical geometry
233 Steady plane waves on a current
The ship-wave pattern
241 Kelvin’s theory
242 Ray theory
Nonlinear problems
The Stokes wave
Nonlinear long waves
261 The method of characteristics
262 The hodograph transformation
Hydraulic jump and bore
Nonlinear waves on a sloping beach
The solitary wave
291 The sech2 solitary wave
292 Integral relations for the solitary wave
Further reading
Exercises
Weakly nonlinear dispersive waves
Introduction
The Korteweg-de Vries family of equations
321 Korteweg-de Vries (KdV) equation
322 Two-dimensional Korteweg-de Vries (2D KdV)
equation
323 Concentric Korteweg-de Vries (cKdV) equation
324 Nearly concentric Korteweg-de Vries (ncKdV)
equation
325 Boussinesq equation
326 Transformations between these equations
327 Matching to the near-field
85
90
93
100
105
108
117
120
134
138
139
146
148
153
156
162
165
171
176
181
182
200
200
204
204
209
211
214
216
219
221
U
2
Completely integrable equa
theory
331 Solution of the Kort
332 Soliton theory for ot
333 Hirota’s bilinear met
334 Conservation laws
Waves in a nonuniform env
341 Waves over a shear
The Bums condition
Ring waves over a s
The Korteweg-de V
Oblique interaction
Further reading
Exercises
3 4 2
3 4 3
3 4 4
3 4 5
Slow modulation of dispersi
The evolution of wave pac
411 Nonlinear Schrödin
412 Davey-Stewartson (
413 Matching between t
NLS and DS equations: so
421 Solution of the Non
422 Bilinear method for
423 Bilinear form of the
424 Conservation laws f
Applications of the NLS a
431 Stability of the Stok
432 Modulation of wave
433 Modulation of wave
Further reading
Exercises
Epilogue
The governing equations w
Applications to the propag
521 Small amplitude ha
Attenuation of the s
Undular bore
Undular bore
5 2 2
5 2 3
5 2 4
mo
mo
Contents
Contents
and the propagation of energy
es on deep water
r variable depth
ity waves of any wave number moving
slope
r a constant slope
y varying environment
plane waves over variable depth
ylindrical geometry
ves on a current
characteristics
transformation
re
sloping beach
ry wave
s for the solitary wave
rsive waves
s family of equations
ries (KdV) equation
1 Korteweg-de Vries (2D KdV)
teweg-de Vries (cKdV) equation
c Korteweg-de Vries (ncKdV)
tion
s between these equations
near-field
69
75
80
85
90
93
100
105
108
117
120
134
138
139
146
148
153
156
162
165
171
176
181
182
Pf
200
200
204
204
209
211
214
216
219
221
5
5 1
5 2
Completely integrable equations: some results from soliton
theory
331 Solution of the Korteweg-de Vries equation
332 Soliton theory for other equations
333 Hirota’s bilinear method
334 Conservation laws
Waves in a nonuniform environment
341 Waves over a shear flow
342 The Burns condition
343 Ring waves over a shear flow
344 The Korteweg-de Vries equation for variable depth
345 Oblique interaction of waves
Further reading
Exercises
Slow modulation of dispersive waves
The evolution of wave packets
411 Nonlinear Schrödinger (NLS) equation
412 Davey-Stewartson (DS) equations
413 Matching between the NLS and KdV equations
NLS and DS equations: some results from soliton theory
421 Solution of the Nonlinear Schrödinger equation
422 Bilinear method for the NLS equation
423 Bilinear form of the DS equations for long waves
424 Conservation laws for the NLS and DS equations
Applications of the NLS and DS equations
431 Stability of the Stokes wave
432 Modulation of waves over a shear flow
433 Modulation of waves over variable depth
Further reading
Exercises
Epilogue
The governing equations with viscosity
Applications to the propagation of gravity waves
521 Small amplitude harmonic waves
522 Attenuation of the solitary wave
523 Undular bore - model I
524 Undular bore - model II
ix
223
225
233
234
243
255
255
261
263
268
277
284
285
297
298
298
305
308
312
312
318
323
325
331
332
337
341
345
345
356
357
359
360
365
374
378
X
Contents
Further reading 386
Exercises 387
Appendices 393
A The equations for a viscous fluid 393
B The boundary conditions for a viscous fluid 397
C Historical notes 399
D Answers and hints 405
Bibliography 429
|
| any_adam_object | 1 |
| author | Johnson, R. S. 1944- |
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| author_facet | Johnson, R. S. 1944- |
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| bvnumber | BV011993175 |
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| ctrlnum | (OCoLC)36423414 (DE-599)BVBBV011993175 |
| dewey-full | 532/.593/0151 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532/.593/0151 |
| dewey-search | 532/.593/0151 |
| dewey-sort | 3532 3593 3151 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV011993175 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:22:26Z |
| institution | BVB |
| isbn | 0521591724 052159832X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008116284 |
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| physical | XIV, 445 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge texts in applied mathematics |
| series2 | Cambridge texts in applied mathematics |
| spellingShingle | Johnson, R. S. 1944- A modern introduction to the mathematical theory of water waves Cambridge texts in applied mathematics Hidromecanica e hidrodinamica larpcal Vloeistofmechanica gtt Water waves - Mathematics Water gtt Water waves Wave-motion, Theory of Mathematisches Modell (DE-588)4114528-8 gnd Soliton (DE-588)4135213-0 gnd Wasserwelle (DE-588)4136091-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4135213-0 (DE-588)4136091-6 (DE-588)4077970-1 |
| title | A modern introduction to the mathematical theory of water waves |
| title_auth | A modern introduction to the mathematical theory of water waves |
| title_exact_search | A modern introduction to the mathematical theory of water waves |
| title_full | A modern introduction to the mathematical theory of water waves R. S. Johnson |
| title_fullStr | A modern introduction to the mathematical theory of water waves R. S. Johnson |
| title_full_unstemmed | A modern introduction to the mathematical theory of water waves R. S. Johnson |
| title_short | A modern introduction to the mathematical theory of water waves |
| title_sort | a modern introduction to the mathematical theory of water waves |
| topic | Hidromecanica e hidrodinamica larpcal Vloeistofmechanica gtt Water waves - Mathematics Water gtt Water waves Wave-motion, Theory of Mathematisches Modell (DE-588)4114528-8 gnd Soliton (DE-588)4135213-0 gnd Wasserwelle (DE-588)4136091-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Hidromecanica e hidrodinamica Vloeistofmechanica Water waves - Mathematics Water Water waves Wave-motion, Theory of Mathematisches Modell Soliton Wasserwelle Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008116284&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005466119 |
| work_keys_str_mv | AT johnsonrs amodernintroductiontothemathematicaltheoryofwaterwaves |