Generation of Mesoscale Variability by Resonant Interaction between a Baroclinic Current and Localized Topography

Abstract

The resonant interaction of a longshore baroclinic current with a topographic feature is investigated, using a quasi-geostrophic two-layer model, where the lower layer is assumed to be deep but is not stagnant. In this model the current may be baroclinically unstable. When a long-wave phase speed is close to zero (in a fixed reference frame), which is found to be realized when the current has almost zero velocity at the coast, there is an enhanced generation of mesoscale variability due to a combination of resonant topographic forcing and baroclinic instability. A forced evolution equation of the KdV-type, which includes an additional coupling term with the lower-layer equation, describes the behavior of the upper layer. On the other hand, the lower-layer motion is governed by a linear vorticity equation, which in turn is coupled to the upper-layer equation. A stability analysis shows that a solitary wave is unstable when a parameter Γ (the phase speed in the absence of any coupling between the two layers) takes values in a certain range determined by considering a linear stability problem. A variety of numerical solutions are presented, covering stable and unstable cases, characterized by the property of the baroclinic current and the forcing mechanism, which is due either to a coastline perturbation or to bottom topography. It is found that upstream and downstream nonlinear waves are generated due to resonant forcing and may be further amplified by baroclinic instability if the wave parameter Γ meets the instability criterion. These destabilized nonlinear waves show very complicated interactive behavior.