Generation of Interfacial Coherent Structures by Internal Waves in Stratified Fluids

Abstract

Large amplitude internal waves in a density stratified fluid are treated numerically. The flow is modeled using the Navier-Stokes system of equations under the Boussinesq approx- imation. The background density profile is two layers of constant density with a smooth transition region, created with the hyperbolic tangent function. The numerical method evaluates derivatives in the vertical and the longitudinal horizontal direction with finite dif- ferences, and in the transverse horizontal with Fourier transforms. Temporal integration is performed using a splitting algorithm. Waves are forced at one boundary to create a self- focusing wave packet so that a large amplitude wave will form away from the wavemaker. The results show that if the amplitude is large, a coherent structure forms at the front of the packet. This structure moves relatively slowly, often slower than the group velocity of all individual waves in the self-focusing packet that created the structure. A second method of wavemaking using a chamber of heavy fluid confirms that large amplitude waves form this coherent structure. Three dimensional simulations suggest that the structure will become three dimensional for long times.