Stability of β-plane Kolmogorov flow

Abstract

We show that the geophysical β-effect strongly affects the linear stability of a sinusoidal Kolmogorov flow. If α denotes the angle between the flow direction and the planetary vorticity gradient then the critical Reynolds’ number, R c( α, β), is zero for β≠0, provided that sin 2α≠0 . In particular, the small β limit is discontinuous: lim β→0 R c (α,β)=0 , rather than the classical value R c (α,0)= 2 . Moreover, though the Kolmogorov flow is non-zonal, the most unstable modes are large-scale quasizonal flows. These results are obtained using asymptotic analysis and confirmed by numerical solution. The simulations show the saturating effects of nonlinearities.