Calculation the internal gravity wave field associated with arbitrary unsteady motion of a source

Abstract

The problem of calculating the linear internal gravity wave field excited by the arbitrary unsteady motion of a point source in a layer of stratified fluid is considered. The solution of this problem makes it possible to investigate the fields of linear internal waves generated under various conditions of motion of the perturbation source, for example, when the source moves at a velocity close to the maximum internal-wave group propagation velocity, or when the motion occurs at variable depth, etc. In certain cases (uniform motion of the source, model density distributions) these problems can be investigated using various asymptotic methods. However, in the linear formulation the exact solution of the problem of internal wave generation by arbitrary moving sources should be the starting point. In most previous studies of this problem, both the internal waves generated by an arbitrary moving source in an exponentially stratified fluid and the internal wave fields induced by a uniformly moving source in a layer of arbitrarily stratified fluid were investigated. In the present study we assume that both the trajectory of the source and the stratification, i.e., the density distribution over depth, are arbitrary.