On the formation of nonlinear internal waves from the gravitational collapse of mixed regions in two and three dimensions

TLDR

The study relates internally generated waves to natural oceanic and atmospheric waves, supporting a possible explanation for observed phenomena. The mechanism involves a mixed fluid region with higher potential energy collapsing toward equilibrium, producing nonlinear internal waves. The collapsing mixed region generates trains of solitary, dispersive waves whose number and amplitude depend on the region’s properties and ambient stratification, with geometry critically shaping wave form and final equilibrium, and wave amplitude may decrease during propagation yet still behave as solitary waves.

Abstract

We show how trains of nonlinear, dispersive wavesIn some of the caaes to be described these are in fact sequences of solitary waves which are ordered by amplitude and which separate in space, as they propagate. In other cases the wave amplitude decreases as the wave propagates, but since the essential balance is between nonlinear steepening and frequency dispersion we feel justified in using the adjective ‘solitary’ to describe them though they violate the clessical description of such waves. can be produced by allowing a region of mixed fluid, with a potential energy greater than its surroundings, to collapse towards its equilibrium state. The number of waves and their amplitude depend on the properties of the mixed region and of the ambient stratification. Three different geometrical configurations have been chosen and while each gives qualitatively the same results the form taken by the generated waves and the final equilibrium shape of the mixed region depend critically on these geometrical factors. We relate the internal waves produced by this mechanism to waves produced in natural systems and show that our observations support at least one possible explanation for those found in the oceans and planetary atmospheres.