Applied and Interdisciplinary Mathematics Seminar

University of Michigan

Fall 2008
Monday, 8 September, 4:10-5:00pm, 3088 East Hall

Kelvin-Helmholtz instability of large amplitude internal solitary waves and a regularized model

Wooyoung Choi

New Jersey Institute of Technology


Abstract

Packets of nonlinear internal waves have been observed in many coastal regions around the world. These wave packets typically generated by the interaction of stratified tidal flow with topographic features are highly nonlinear and their wave amplitudes often exceed 100 m. In this work, we study large amplitude internal solitary waves in a system of two constant density layers using a strongly nonlinear long wave model. While steady solitary wave solutions of the model show excellent agreement with numerical solutions of the Euler equations and laboratory experiments, a local stability analysis reveals that the time-dependent inviscid model suffers from the Kelvin-Helmholtz instability due to a tangential velocity discontinuity across the interface. To suppress this undesirable short wave instability that is often absent in real experiments, an attempt is made to regularize the model by modifying the short wave behavior of the dispersion relation and introducing the effect of viscosity.