Influence of the Elastic Base of a Basin on the Propagation of Waves on the Water Surface
S. Yu. Dobrokhotov, O. L. Tolstova, S. Ya. Sekerzh–Zen’kovich, C. A. Vargas · Russian Journal of Mathematical Physics · 2018
A layer of an ideal liquid located on an elastic half-space (with a flat unperturbed boundary) is considered in the linear approximation. At the zero time moment, a localized perturbation of the displacement vector occurs in the elastic half-space, and this perturbation, after some time, leads to a modification (perturbation) of the interface between the water and the crust, which, in turn, leads to a localized perturbation on the surface of the liquid and to the occurrence of surface waves. We are interested in the following question: to what extent does getting rid of the stiffness of the bottom and replacing it by an elastic base influence the speed of propagation of the front of the long wave and its profile under the assumption that the initial perturbation is given immediately on the free surface of the liquid?