Traveling Waves in Shallow Seas of Variable Depths
Efim Pelinovsky, О. В. Капцов
Abstract
The problem of the existence of traveling waves in inhomogeneous fluid is very important for enabling an explanation of long-distance wave propagations such as tsunamis and storm waves. The present paper discusses new solutions to the variable-coefficient wave equations describing traveling waves in fluid layers of variable depths (1D shallow-water theory). Such solutions are obtained by using the transformation methods when variable-coefficient equations can be reduced to the constant coefficient equation when the existence of traveling waves is evident. It is shown that there is a wide class of monotonic bottom profiles (discrete set) that allow the existence of traveling waves that are not reflected in a strongly inhomogeneous water medium. Their temporal shape changes with distance, mainly near the water–land boundary (shoreline). Traveling waves can transfer the wave energy over a long distance that is often observed at the transoceanic propagation of tsunami waves.