Three-dimensional water-wave scattering in two-layer fluids
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In this article, the problem of wave radiation and scattering by a submerged sphere in either the upper or lower layer of a single-layer fluid is solved using multipole expansions, where the reciprocity relations connecting the various hydrodynamic quantities that arise are systematically extended to the two-fluid case.Abstract:
We consider, using linear water-wave theory, three-dimensional problems concerning the interaction of waves with structures in a fluid which contains a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density. For such a situation time-harmonic waves can propagate with two different wavenumbers K and k. In a single-layer fluid there are a number of reciprocity relations that exist connecting the various hydrodynamic quantities that arise, and these relations are systematically extended to the two-fluid case. The particular problems of wave radiation and scattering by a submerged sphere in either the upper or lower layer are then solved using multipole expansions.read more
Citations
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Scattering of oblique waves in a two-layer fluid
TL;DR: In this article, the problem of wave scattering by a horizontal circular cylinder in either the upper or lower layer of a fluid is solved using multipole expansions, where wave scattering can propagate with two different wavenumbers.
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Flexural gravity wave problems in two-layer fluids
J. Bhattacharjee,Trilochan Sahoo +1 more
TL;DR: In this article, expansion formulae for flexural gravity wave problems in two-layer fluids are developed in both the cases of water of finite and infinite depths, and relations based on Green's identity are derived for the reflection and transmission coefficients in surface and interface modes.
Journal ArticleDOI
Waves past porous structures in a two-layer fluid
S.R. Manam,Trilochan Sahoo +1 more
TL;DR: In this paper, Havelock's type of expansion theorems are utilized to derive analytical solutions for the radiation or scattering of oblique water waves by a fully extended porous barrier in both the cases of finite and infinite depths of water in two-layer fluid with constant densities.
Journal ArticleDOI
Wave scattering in a two-layer fluid of varying depth
P. G. Chamberlain,D. Porter +1 more
TL;DR: In this paper, a variational technique is used to construct a particular type of approximation which has the effect of removing the vertical coordinate and reducing the problem to two coupled partial differential equations in two independent variables.
Journal ArticleDOI
Water wave radiation by a sphere submerged in water with an ice-cover
Dilip Kumar Das,B. N. Mandal +1 more
TL;DR: In this article, the problem of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice cover was formulated using the multipoles method, with the ice cover being modeled as an elastic plate of very small thickness.
References
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Handbook of Mathematical Functions
Book
The applied dynamics of ocean surface waves
TL;DR: In this article, the authors present selected theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering, all from a deterministic point of view, and the bulk of the material deals with the linearized theory.
Journal ArticleDOI
Multipole expansions in the theory of surface waves
R. C. Thorne,F. Ursell +1 more
TL;DR: In this article, the authors considered the problem of the generation of surface waves by a submerged circular cylinder and used a series of complex potential functions arising from multipoles at the centre of the cylinder, but the velocity potential of the motion could have been described, without the introduction of the stream function.
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The interaction of waves with horizontal cylinders in two-layer fluids
TL;DR: In this article, the authors considered two-dimensional problems based on linear water wave theory concerning the interaction of waves with horizontal cylinders in a fluid consisting of a layer of finite depth bounded above by a free surface and below by an infinite layer of fluid of greater density.
Journal ArticleDOI
The radiation and scattering of surface waves by a vertical circular cylinder in a channel
Christopher Linton,D. V. Evans +1 more
TL;DR: In this paper, the problem of the radiation and scattering of surface gravity waves by a vertical circular cylinder placed on the centreline of a channel of width 2 d and depth H, and either extending from the bottom through the free surface or truncated so as to fill only part of the depth.