Trapped Vortex Cores in Internal Solitary Waves Propagating in a Thin Stratified Layer Embedded in a Deep Homogeneous Fluid

Abstract

An asymptotic model for long large-amplitude internal solitary waves with a trapped core, propagating in a narrow layer of nearly uniformly stratified fluid embedded in an infinitely deep homogeneous fluid is presented. The case of a mode one asymmetric wave with an amplitude slightly greater than the critical amplitude, for which there is incipient overturning, is considered. A vortex core located near the point at which this incipient breaking occurs is then incorporated. The effect of the vortex core is to introduce into the governing equation for the wave amplitude an extra nonlinear term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude. The result is that as the wave amplitude increases above the critical amplitude, the wave broadens, which is in marked contrast to the case of small amplitude waves where a sharpening of the wave crest normally occurs. The limiting form of the broadening wave is a deep fluid bore. The wave speed is found to depend nonlinearly on the wave amplitude.