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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 5, Pages 737-746

Water waves generated by disturbances at an ice cover

Physics and Applied Mathematics Unit, Physics and Earth Sciences Division, Indian Statistical Institute, 203 Barrackpore Trunk Road, Calcutta 700 108, India

Received 13 June 2004; Revised 30 November 2004

Copyright © 2005 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.


This paper is concerned with two-dimensional unsteady motion of water waves generated by an initial disturbance created at an ice sheet covering the water. The ice cover is modeled as a thin elastic plate. Using linear theory, the problem is formulated as an initial value problem for the velocity potential describing the motion in the liquid. In the mathematical analysis, the Laplace and Fourier transform techniques have been utilized to obtain the depression of the ice-covered surface in the form of an infinite integral. For the special case of initial disturbance concentrated at the origin, taken on the ice cover, this integral is evaluated asymptotically by the method of a stationary phase for a long time and large distance from the origin. The form of the ice-covered surface is graphically depicted for two types of initial disturbances.