A Study of Stratospheric Vacillations and Sudden Warmings on a β-Plane. Part I: Single Wave-Mean Flow Interaction

Abstract

A ?-plane model of the stratosphere is used to investigate the planetary-wave amplitude vacillations first reported by Holton and Maw (1976). This model differs from theirs in allowing more horizontal modes. For low surface wave amplitudes, a new class of solutions is found which exhibits a stationary, partially reflecting critical line at steady state. The critical line equilibrates at lower altitudes as the wave forcing is increased. Vacillating solutions occur when the steady state critical line occurs near the lower boundary. The maximum wave amplitude and the maximum steady-state wave amplitude found in the model are in the ratio of 2:1, in good agreement with theoretical predictions. The maximum wave amplitude never exceeds 2200 gpm which is quite close to the saturation limit predicted by Schoeberl (1982a). An analysis of the statistics of slowly and rapidly vacillating flows shows that both the wave and zonal mean variances are important in determining the time mean, zonal mean dynamics of the upper stratosphere.