Trapped modes in a channel containing three layers of fluids and asubmerged cylinder

Chakrabarti, A and Daripa, P and Hamsapriye, * (2005) Trapped modes in a channel containing three layers of fluids and asubmerged cylinder. In: Zeitschrift fur Angewandte Mathematik und Physik, 56 (6). pp. 1084-1097.

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Abstract

The problem of existence of trapped waves in fluids due to a cylinderis investigated for the hydrodynamic set-up which involves a horizontal channel of infinite length and depth and of finite width containing three layers of incompressible fluids of different constant densities.The set-up also contains a cylinder which is impermeable, fully immersed in the bottom (lower-most) fluid layer of infinite depth, and extends across the channel with its generators perpendicular to the side walls of the channel. When the ratios of the densities of the adjacent fluids differ from unity by sufficiently small quantities, the underlying mathematical problem reduces to a generalized nonline are igenvalue problem involving a cubic polynomial-cum-operator equation.The perturbation analysis of this eigenvalue problem suggests existence of three distinct modes with different frequencies: one of the order of one persisting at the free surface, and the other two of the order of the density ratio (except for modulo one) persisting at the two internal interfaces. The correlation between these results for the three-layer case and very recent numerical results of other authors in the two-layer case has also been addressed.

Item Type:	Journal Article
Publication:	Zeitschrift fur Angewandte Mathematik und Physik
Publisher:	Birkhauser Verlag AG
Additional Information:	Copyright for this article belongs to Birkhauser Verlag AG.
Keywords:	Trapped waves;potential flows;interfacial flows
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	09 Dec 2005
Last Modified:	19 Sep 2010 04:21
URI:	http://eprints.iisc.ac.in/id/eprint/4355

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