The linear stability of zonal flows superposed upon a sinusoidal, slightly supercritical background flow in an equivalent-barotropic quasi-geostrophic model on a β plane is investigated using asymptotic analysis. Consistent with results of full numerical simulations, all the steady isolated zonal jet solutions were found to be linearly unstable, and specifically, the mode independent of longitudinal direction was found to be most unstable, even when the amplitude equation of the zonal flows has longitudinal dependence.
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