For 2D Navier-Stokes shear flows on the beta-plane, long-wave stability is governed by a rotation-modified norm of the shear profile, with instability when that norm exceeds the viscosity.
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Long-Wave Stability And Instability Of Periodic Shear Flows For The 2D Navier-Stokes Equations On The $\beta$-Plane
For 2D Navier-Stokes shear flows on the beta-plane, long-wave stability is governed by a rotation-modified norm of the shear profile, with instability when that norm exceeds the viscosity.