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An alternative approach to study nonlinear inviscid flow over arbitrary bottom topography

Panda, Srikumar and Martha, SC and Chakrabarti, A (2016) An alternative approach to study nonlinear inviscid flow over arbitrary bottom topography. In: APPLIED MATHEMATICS AND COMPUTATION, 273 . pp. 165-177.

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Official URL: http://dx.doi.org/10.1016/j.amc.2015.09.086

Abstract

This paper deals with a new approach to study the nonlinear inviscid flow over arbitrary bottom topography. The problem is formulated as a nonlinear boundary value problem which is reduced to a Dirichlet problem using certain transformations. The Dirichlet problem is solved by applying Plemelj-Sokhotski formulae and it is noticed that the solution of the Dirichlet problem depends on the solution of a coupled Fredholm integral equation of the second kind. These integral equations are solved numerically by using a modified method. The free-surface profile which is unknown at the outset is determined. Different kinds of bottom topographies are considered here to study the influence of bottom topography on the free-surface profile. The effects of the Froude number and the arbitrary bottom topography on the free-surface profile are demonstrated in graphical forms for the subcritical flow. Further, the nonlinear results are validated with the results available in the literature and compared with the results obtained by using linear theory. (C) 2015 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ELSEVIER SCIENCE INC, 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA
Keywords: Integral equation; Dirichlet problem; Nonlinear theory; Inviscid flow
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 02 Jan 2016 09:45
Last Modified: 02 Jan 2016 09:45
URI: http://eprints.iisc.ac.in/id/eprint/53027

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