We compute the irrotational motion of two fluids with a horizontal plane surface of separation, under gravity. The fluids are nonviscous and incompressible, the upper one of finite depth with a free surface; they contain a line singularity or a point singularity. We obtain the velocity potentials for each singularity located in the upper or the lower fluid; if the upper depth tends to infinity, known results are recovered. © 1983, Hindawi Publishing Corporation. All rights reserved.

R N CHAKRABARTI

B MANDAL

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Singularities in a two-fluid medium

International Journal of Mathematics and Mathematical Sciences

Two dimensional scattering of linear water wave by thin vertical permeable plate in a two-layer fluid with free surface is considered. The permeable barrier is completely submerged in the upper layer of finite depth over a layer whose depth is either infinite or finite. For discontinuity in the potential across the plate, we use Green's integral theorem to formulate the problem in terms of a hypersingular integral equation. A collocation method using a finite series of Chebyshev polynomials of second kind have been introduced to get the unknown difference potential numerically. The reflection and transmission coefficients for surface and internal modes are computed as an integral involving difference potentials. The proportion of reflected and transmitted energies of both the wavenumbers are calculated. Moreover, amount of energy dissipated due to the presence of permeable plate in the upper layer are obtained. Numerical results are calculated and depicted graphically against the wavenumber for various non-dimensionalized parameters. © 2018 Elsevier Ltd

Ocean Engineering

Effects of vertical porous barrier on progressive waves in a two layered fluid

The present study deals with two dimensional scattering of linear water wave by a thin submerged plate in a two layered fluid. The fluid domain considered here is bounded above by a free surface. For discontinuity in the potential across the plate, we use Greens integral theorem to formulate the problem in terms of a hypersingular integral equation. A collocation method using a finite series of Chebyshev polynomials of second kind have been introduced to get the unknown difference potential numerically. The reflection and transmission coefficients for surface mode are computed as integral involving difference potentials. The proportions of reflected and transmitted energies are calculated. © 2018 Author(s).

AIP Conference Proceedings

Wave scattering by a submerged plate in a two-layer fluid of finite depth

The scattering of plane surface waves by bottom undulations in a three-layer channel of different constant densities is investigated here by using a simplified perturbation analysis. In such a three layer fluid there exists waves of two different modes propagate along each of the interfaces. In the process of obtaining solution for the problem a Fourier transform technique is employed to derive the first-order corrections of the reflection and transmission coefficients in terms of integrals involving the shape function representing the bottom elevation. For sinusoidal undulations, these coefficients are plotted graphically to illustrate the energy transfer between the waves of different modes induced by the bottom undulations. It is shown that the scattering phenomena effected by the change in different parameters, viz, the porous effect parameter, the number of ripple present at the bottom and the depth of the lower layer.

JOURNAL OF MARINE SCIENCE AND TECHNOLOGY

Wave scattering by uneven porous bottom in a three layered channel

Velocity potentials describing the irrotational infinitesimal motion of two superposed inviscid and incompressible fluids under gravity with a horizontal plane of mean surface of separation, are derived due to a vertical line source present in either of the fluids, whose strength, besides being harmonic in time, varies sinusiodally along its length. The technique of deriving the potentials here is an extension of the technique used for the case of only time harmonic vertical line source. The present case is concerned with the two-dimensional modified Helmholtz’s equation while the previous is concerned with the two-dimensional Laplace’s equation. © 1986, Hindawi Publishing Corporation. All rights reserved.

Journal	International Journal of Mathematics and Mathematical Sciences
Publisher	-
ISSN	0161-1712
Open Access	Yes