Title:
Water wave scattering by barriers
Personal Author:
Publication Information:
Boston, FL : WIT Press, 2000
Physical Description:
390 p. : ill. ; 24 cm.
ISBN:
9781853126239
Added Author:
Available:*
Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000010197387 | QA927 M94 2000 | Open Access Book | Book | Searching... |
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Summary
Summary
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.
Table of Contents
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 |