Aplikácia integrálnych transformácií na určenie vzťahu rozptylu morskej vlny od nadmorskej výšky hladiny mora

Abstract

The focus of this paper is the linear problem of gravity waves on the surface of a viscous incompressible fluid with a constant finite depth. This problem arises when the free surface is in a state of rest and there is a finite perturbation and a given normal pressure on it. We resolve the time evolution of the initial surface perturbation, or the classical linear Cauchy-Poisson problem, in the presence of a uniformly vorticous shear current beneath the surface. The solution is general, including the effects of gravity, surface tension, and constant finite depth. The main goal of this paper is to study such a problem, which appears to be important and interesting from a mathematical as well as a physical point of view. The problem is solved by using the Laplace and Henkel transformations, and we get an integral solution.