A note on surface water waves for finite depth in the presence of an ice-cover

Document Type

Article

Publication Date

11-1-2003

Abstract

A class of boundary value problems involving propagation of two-dimensional surface water waves, associated with water of uniform finite depth, against a plane vertical wave maker is investigated under the assumption that the surface is covered by a thin sheet of ice. It is assumed that the ice-cover behaves like a thin isotropic elastic plate. Then the problems under consideration lead to those of solving the two-dimensional Laplace equation in a semi-infinite strip, under Neumann boundary conditions on the vertical boundary as well as on one of the horizontal boundaries, representing the bottom of the fluid region, and a condition involving upto fifth order derivatives of the unknown function on the top horizontal ice-covered boundary, along with the two appropriate edge-conditions, at the ice-covered corner, ensuring the uniqueness of the solutions. The mixed boundary value problems are solved completely, by exploiting the regularity property of the Fourier cosine transform.

Identifier

26844449446 (Scopus)

Publication Title

Indian Journal of Pure and Applied Mathematics

ISSN

00195588

First Page

1631

Last Page

1644

Issue

11

Volume

34

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