Barotropic Instability of Rossby Wave Motion

Zonal flow resembling zonally averaged tropospheric motion in middle latitudes is usually barotropically stable, but zonal flow together with superposed neutral Rossby waves may be unstable with respect to further perturbations. Rossby's original solution of the barotropic vorticity equation is tested for stability, using beta-plane geometry. When the waves are sufficiently strong or the wavenumber is sufficiently high, the flow is found to be unstable, but if the flow is weak or the wavenumber is low, the beta effect may render the flow stable. The amplification rate of growing perturbations is comparable to the growth rate of errors deduced from large numerical models of the atmosphere. The Rossby wave motion together with amplifying perturbations possesses jet-like features not found in Rossby wave motion alone. It is suggested that barotropic instability is largely responsible for the unpredictability of the real atmosphere.