Nonlinear baroclinic instability of a continuous zonal flow of viscous fluid

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Abstract
Nonlinear instability of a zonal flow of slightly viscous Boussinesq fluid in a rapidly rotating frame is studied mathematically by the method of normal mode cascade, the flow being along a rectangular channel with horizontal and vertical rigid walls. Viscosity is represented approximately by supposing that its only effects occur in Ekman layers near the top and bottom walls of the channel, after the linear model of Barcilon. Self-interaction of one slightly unstable mode is found to lead to equilibration with supercritical instability. Also, interactions of two slightly unstable modes plausibly lead to equilibration. These results are related to the literature of experiments on differentially heated, rotating annuli.

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