The wave-problem of cauchy and poisson for finite depth and slightly compressible fluid

Abstract

The present paper is in some respects a completion of a former paper on water waves resulting from a given disturbance. The following article is devoted to a numerical discussion of a solution, previously given, of the normal Cauchy-Poisson problem for finite constant depth of fluid. The last part of the paper contains a detailed treatment of compressible fluids, with a view to elucidating the initial stages of the spreading out of a disturbance initiallu confined to a limited region of the fluid. It is found that a very general case of propagation is capable of formal solution. 2. Numerical Discussion of the Cauchy-Poisson Problem for Finite Depth . The serial solution given in the previous paper lends itself to a certain extent to numerical treatment, though not so well as for the case of infinite depth, which has been so completely discussed by Lamb. In the general case there does not seem to be any general transformation to facilitate the calculation, so that we have to rely on the direct use of the series. The solution referred to may be briefly recapitulated as follows.