Coupled Ostrovsky equations for internal waves on a shear flow

Karima Khusnutdinova

Department of Mathematical Sciences, Loughborough University


We study the behaviour of weakly nonlinear oceanic internal waves in the presence of background rotation and shear flow, when two distinct linear long wave modes have nearly coincident phase speeds. The waves are described by a system of coupled Ostrovsky equations, derived from the full set of Euler equations for incompressible density stratified fluid with a free surface and rigid bottom boundary conditions. We show that in the generic case, in the absence of the shear flow, initial solitary-like waves are destroyed and replaced by two coupled nonlinear wave packets, being the counterpart of the same phenomenon in the single Ostrovsky equation. I will also discuss results obtained when there is a three layer shear flow, when the dynamics is much more diverse.


References:

[1] A. Alias, R.H.J. Grimshaw, K.R. Khusnutdinova, On strongly interacting internal waves in a rotating ocean and coupled Ostrovsky equations, Chaos 23 (2013) 023121.

[2] A. Alias, R.H.J. Grimshaw, K.R. Khusnutdinova, Coupled Ostrovsky equations for internal waves in a three layer shear flow, in preparation.