The effect of a sudden change of shape of the bottom of a slightly compressible ocean

Abstract

When a block on the rigid bottom of a layer of slightly compressible gravitating liquid is instantaneously jerked upwards, acoustic and gravity waves are developed. In this paper a two-dimensional problem is set up, with an infinite-strip block in a layer of uniform depth. There are two distinct regions in space and time; in one (the first in time), the acoustic disturbance predominates with gravity entering as a perturbation, in the other the gravity disturbance is dominant, with compressibility producing a small correction to the motion. In both cases, the ratio of the velocities of long gravity waves and of sound in the medium characterizes the perturbation terms. The form of the acoustic pulses from a source of this type appears to be of theoretical interest, as point and line sources are usually treated in the literature. The gravity waves are akin to Cauchy— Poisson waves and have been much studied in connexion with tsunamis and ocean waves in general, but the treatment of the compressibility effect is thought to be original.