Local instabilities of weakly non-parallel large-scale flows: Wkb analysis

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Abstract
In slightly viscous rotating stratified systems weak potential vorticity sources can excite finite amplitude response when the group velocity of the long waves vanishes. This mechanism is used, in a two layer fluid, to generate steady state solutions that can be characterized as currents. The currents are strongly sheared in both the vertical and the meridional directions but they vary slowly in the zonal direction. Numerical simulations reveal that the currents are unstable with respect to small perturbations and that the unstable response is dominated by trapped eigenmodes. A WKB analysis jointly with a second order turning point problem are used to derive a consistent description of the spatial and temporal characteristics of the unstable eigenmodes. The stability analysis is applicable to zonally varying basic states whose zonal gradient vanishes at some isolated points of the flow domain.

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