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International Journal of Mathematics and Mathematical Sciences
Volume 9, Issue 1, Pages 175-184
http://dx.doi.org/10.1155/S0161171286000200

Two-dimensional source potentials in a two-fluid medium for the modified Helmholtz's equation

Department of Applied Mathematics, University College of Science, 92, A. P. C. Road, Calcutta 700 009, India

Received 10 March 1985

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.