Long interfacial gravity wave-induced short-wave instabilities

In two-layered density stratified geophysical flows, the shear produced by long interfacial gravity waves can render short waves unstable. The two-layered oscillating tank configuration considered in this study provides a simplified analogue of the realistic setting. We show that the equation governing the evolution of linear perturbations on the density interface is a Schrödinger-type ODE with a periodic potential. A single nondimensional parameter β governs the stability condition, and instability arises when β>1/4. When this instability condition is satisfied, the flow is still stable for an initial period but finally tunnels into the unstable region after reaching the time marking the turning point. We also provide a comparison with actual oceanographic settings to obtain a physical perspective of the key parameters.

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