Thursday 05 Jul 2018: Fast and slow resonant triads in the two layer rotating shallow water equations
Alex Owen - University of Exeter
The one-layer rotating shallow-water equations are a commonly used model reduction of the stratified rotating flows. Here we extend this to a two-layer fluid system where both interfaces are free. We take the commonly used quasigeostrophic limit, while maintaining the non-geostrophic inertia-gravity wave modes, to investigate the full set of wave interactions in the system. Past analysis of the wave interactions in this system has fixed the top layer using a rigid lid assumption. Allowing the second layer to have a completely free interface we analyse the triad resonances found amongst the gravity wave interactions, finding that new resonances are permitted. Consideration of these resonances shows some interesting features that depend on the Burger number of the system. These resonances include interactions between large and small wave numbers, with implications in geophysical fluid dynamics.