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

We analytically obtain steady isolated zonal jet solutions of the evolution equation of zonal flows on a β 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 β plane or a rotating sphere might be due to the intrinsic instability of the zonal jets.