Qualitative difference between large waves in deep and shallow fluid formulations

Abstract

The note addresses a qualitative difference between shallow (vertically confined) and deep (vertically non-confined) fluid geometries for stationary internal solitary waves. It is shown that in a deep fluid, the propagation velocity of large amplitude wave (with a vortex inside) is greater than the velocity predicted by small but finite amplitude theory, known as the Benjamin-Ono model. This effect has been found both asymptotically and experimentally. For the case of a shallow fluid, the situation is qualitatively different. The speed of a wave with vortex inside is smaller than that predicted by the Korteweg-de Vries theory. The reported observation could distinguish wave motions in shallow (confined) and deep (non-confined) geometries and seems to be important in a variety of applications.