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Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current
Curtis Hooper, Karima Khusnutdinova, Roger Grimshaw
We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear flow. The far-field modal and amplitude equations for the ring waves are prese…
Quartet, higher order and near resonant interactions in nonlinear wave equations
Alex Owen, Roger Grimshaw, Beth Wingate
Motivated by problems arising in geophysical fluid dynamics, we investigate resonant and near resonant wave interactions in nonlinear wave equations with quadratic nonlinearity, We…
Fast and slow resonant triads in the two layer rotating shallow water equations
Alex Owen, Roger Grimshaw, Beth Wingate
In this paper we examine triad resonances in a rotating shallow water system when there are two free interfaces. This allows for an examination in a relatively simple model of the…