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The authors study the stability of a barotropic sinusoidal meridional flow on a plane. Because of bottom drag and lateral viscosity, the system is dissipative and forcing maintains a basic-state velocity that carries fluid across the planetary vorticity contours; this is a simple model of forced potential vorticity mixing. When the Reynolds number is slightly above the stability threshold, a perturbation expansion can be used to obtain an amplitude equation for the most unstable disturbances. These instabilities are zonal flows with a much larger length scale than that of the basic state.
Manfroi et al. (Mon,) studied this question.
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