Water wave scattering by barriers

Title:

Personal Author:

Mandal, B. N.

Publication Information:

Boston, FL : WIT Press, 2000

Physical Description:

390 p. : ill. ; 24 cm.

ISBN:

9781853126239

Subject Term:

Water waves -- Mathematical models

Scattering (Mathematics)

Added Author:

Chakrabarti, A.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010197387	QA927 M94 2000	Open Access Book	Book	Searching... Unknown

In this unique volume the authors review the development of the subject, virtually from its inception. Details of much of the research work carded out in the linearized theory of water waves concerning problems of water wave scattering by barriers is incorporated.

Preface	p. ix
1 Introduction	p. 1
2 The basic equations	p. 9
2.1 Linearized theory of water waves	p. 9
2.2 Solutions for water wave potential	p. 13
2.3 Two superposed fluids	p. 17
2.4 The surface water waves and the scattering problems	p. 22
2.5 Source potentials	p. 26
3 Some important mathematical concepts and results	p. 37
3.1 Fourier analysis	p. 37
3.2 Complex function theory	p. 58
3.3 Riemann Hilbert problems	p. 59
3.4 Some aspects of the Wiener-Hopf technique	p. 62
3.5 Some aspects of linear singular integral equations	p. 68
3.6 Hypersingular integral equation	p. 78
3.7 Solutions of dual integral equations	p. 85
3.8 Galerkin's method	p. 98
3.9 Values of certain definite integrals	p. 104
4 Explicit solutions to some barrier problems	p. 109
4.1 Description of the physical problems	p. 109
4.2 Method based on Havelock's expansion of water wave potential	p. 111
4.3 Water wave scattering by a partially immersed plate	p. 115
4.4 Water wave scattering by a submerged barrier	p. 120
4.5 Water wave scattering by a submerged plate	p. 124
4.6 Water wave scattering by a thin vertical wall with a submerged gap	p. 131
4.7 Method based on the use of Green's integral theorem	p. 138
4.8 Reduction method	p. 142
4.9 Method based on complex variable theory	p. 146
5 Vertical wall with a narrow gap, approximate solution	p. 153
5.1 Description of the problem	p. 153
5.2 Method of matched asymptotic expansion	p. 154
5.3 Method based on approximate solution of integral equation	p. 160
6 Oblique wave scattering by barriers	p. 165
6.1 Description of the physical problems	p. 165
6.2 Use of Wiener-Hopf technique	p. 167
6.3 Perturbation about normal incidence	p. 176
6.4 Single-term Galerkin approximation	p. 192
7 Nearly vertical barriers and special boundary value problems	p. 207
7.1 Description of the physical problems	p. 207
7.2 Integro-differential equation formulation	p. 209
7.3 Solution by a perturbational analysis	p. 215
7.4 Use of Havelock's expansion to evaluate R[subscript 1]	p. 221
7.5 Special boundary value problems and integral identities	p. 224
7.6 Method based on Havelock's expansion	p. 224
7.7 Method based on Riemann Hilbert problem	p. 236
8 Thin vertical barriers in finite depth water	p. 247
8.1 Single barrier problems	p. 247
8.2 Basis functions in multi-term Galerkin approximations for barrier problems	p. 261
8.3 Double barrier problems	p. 264
9 Thick rectangular barriers in finite depth water	p. 287
9.1 Water wave scattering problems involving thick barriers	p. 287
9.2 Expressions for M[superscript s,a](y, u)	p. 297
9.3 The basis functions	p. 299
9.4 Expressions for [characters not reproducible] etc.	p. 304
9.5 Numerical results	p. 308
10 Interface wave scattering by barrier	p. 319
10.1 Vertical barrier submerged in lower fluid	p. 320
10.2 Inclined plate submerged in lower fluid	p. 334
11 Incoming water waves against a vertical cliff	p. 343
11.1 Normally incident waves	p. 344
11.2 Obliquely incident waves	p. 345
11.3 Effect of surface tension	p. 348
12 Second-order wave scattering	p. 351
12.1 "Second-order" mathematical analysis	p. 352
12.2 "Second-order" reflection and transmission coefficients	p. 357
Appendix	p. 361
A Singular integral equations of the first kind with Cauchy type kernel	p. 361
B A particular singular integral equation	p. 368
Bibliography	p. 373
Indexes	p. 385
Subject index	p. 387
Author index	p. 389

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