Linear stability of steady zonal jet flows induced by a small-scale forcing on a ββ plane

We analytically obtain steady isolated zonal jet solutions of the evolution equation of zonal flows on a ββ plane with a homogeneous zonal flow and a small-scale sinusoidal transversal flow in the background, derived by Manfroi and Young (1999) [9]. It is shown that these steady zonal jet solutions are all linearly unstable. Numerical time integrations of the evolution equation also confirm that the perturbed unstable steady solution becomes a uniform flow in the long run. These results suggest that mergers/disappearances of zonal jets superposed upon background forced two-dimensional turbulence on a ββ plane or a rotating sphere might be due to the intrinsic instability of the zonal jets.

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► Dynamics of zonal flow with a background sinusoidal transversal flow is considered.
► Steady solutions of isolated zonal jets are analytically obtained.
► These steady zonal jet solutions are all linearly unstable.
► The perturbed unstable steady solutions become uniform flows as time goes on.
► Results imply zonal barotropic flow is unstable due to the background turbulence.