Roxana Tiron, University of North Carolina at Chapel Hill

New solutions for internal waves at the interface between two fluids

Abstract:  Internal waves are among the most intriguing phenomena in ocean and atmosphere dynamics and  had recently became accessible to analysis through new powerful instrumentation techniques. A system comprising two fluids of different densities is the simplest
that supports internal  wave motion and offers a good approximation for physical relevant configurations.

We obtain new forms for periodic traveling  waves at the interface of such a system. The model used is an asymptotic model deduced by Choi and Camassa; the model supports large amplitude motion and bidirectional wave propagation. Under the assumption of a wave of permanent form traveling with constant speed and making use of physically dictated constraints, the governing equations reduce to a quadrature, whose solution is expressible using hyperelliptic functions. Considering unidirectional wave propagation and limiting the amplitude, an evolution equation for the interface deformation can be deduced. In analogy with the bidirectional model, traveling wave solutions can be computed by quadratures.

Explicit forms for periodic waves are extremely useful in the analysis of slowly varying wave trains.

Advisor: Roberto Camassa (UNC)