Response of a floating ice sheet due to a moving load in the presence of an undulating sea bottom

This work studies how waves are generated due to a moving load activated on a floating ice sheet in the presence of an undulating sea bottom. This study is concerned with the two-dimensional situation in which a line load is considered as the moving load on the ice sheet. The Fourier transform technique is used to solve the governing equation, which is derived from potential flow theory. A perturbation method is utilized to study the effect of the moving load and the undulating sea-bed in the form of a sinusoidal ripple bed. Expressing the moving load in the form of a Dirac delta function and a Heaviside unit step function, the ice sheet deflection is obtained through an integral for which the asymptotic contribution associated with stationary points for various load speed regimes is obtained. Various load speeds are found to be responsible for altering the deflection of the ice sheet. During the study of the effect of the undulating sea-bed, the ice behavior is observed to be closer to that of a flat sea-bed when the number of ripples of the undulation increases. In addition, a noticeable difference arises in the ice sheet deflection around the load when the number of ripples varies. In all results, the phenomenon of Bragg resonance is accounted for. The findings of this work provide valuable information on the complex interplay among the ice sheet, sea-bed undulation, and external forcing, contributing significantly to the understanding of wave dynamics in ice-covered environments.