Solutions in Straits of Varying Width and Depth

摘要

In order to analyze data on the creation and propagation of large solitary waves in marine straits, a theoretical model extending previous one-dimensional models to the case of straits with varying width and depth, and nonvanishing vorticity, was developed. Starting from the Euler equations for a three dimensional homogeneous incompressible inviscid fluid, a generalized Kadomtsev-Petviashvili equation (GKP) together with its appropriate boundary conditions is derived in the quasi one-dimensional long wave and shallow water approximation. The coefficients of this equation depend on the form of the bottom and on the vorticity; the sides of the straits figure only on the boundary conditions. Under certain restrictions on the vorticity and the geometry of the straits the GKP is reduced to one of several completely integrable partial differential equations, in order to study the evolution of solitons which originate in the straits.