Abstract
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.
Highlights
The two-dimensional problems concerning generation of water waves due to a prescribed initial displacement or impulse mostly concentrated at a point were discussed in treaties of Lamb [4] and Stoker [6] within the framework of the linearized theory of water waves
The ice cover is assumed to consist of a thin ice sheet of small thickness h, say, of which still a smaller part is immersed in water, the ice sheet being composed of materials having elastic properties
This integral is evaluated for large distance and long time for the case when the initial disturbance is concentrated at the origin
Summary
The two-dimensional problems concerning generation of water waves due to a prescribed initial displacement or impulse mostly concentrated at a point were discussed in treaties of Lamb [4] and Stoker [6] within the framework of the linearized theory of water waves. Kranzer and Keller [3] considered axially symmetrical initial surface disturbance in water of finite depth and compared the theory with experimental results. The ice cover is assumed to consist of a thin but uniform distribution of noninteracting materials with no elastic property, known as an inertial surface (e.g., broken ice). Mandal [5] considered generation of water waves due to initial disturbances at such an inertial surface. We consider the problem of generation of water waves in an ocean of infinite depth covered by such. In the absence of the ice cover, this reduces to the classical result This integral is evaluated for large distance and long time for the case when the initial disturbance is concentrated at the origin. The asymptotic form of the depression is displayed graphically for various values of the ice cover parameter, in a number of figures, and compared with the case when there is no ice cover
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