Water waves generated due to initial axisymmetric disturbances in water with an ice-cover

This paper is concerned with the generation of water waves due to prescribed initial axisymmetric disturbances in a deep ocean with an ice-cover modelled as a thin elastic plate. The initial disturbances are either in the form of an impulsive pressure distributed over a certain region of the ice-cover or an initial displacement of the ice-cover. Assuming linear theory, the problem is formulated as an initial-value problem in the velocity potential describing the ensuing motion in the fluid. In the mathematical analysis, the Laplace and Hankel transform techniques have been utilised to obtain the deformation of the ice-covered surface as an infinite integral in each case. The method of stationary phase is used to evaluate the integral for large values of time and distance. Figures are drawn to show the effect of the presence of ice-cover on the wave motion.