A Numerical Study of the Role of Wave-Wave Interactions during Sudden Stratospheric Warmings

Abstract

In this study the role of nonlinear wave-wave interactions is investigated by performing two experiments using a numerical model adapted from that of Holton (1976). In the first experiment the model simulates a sudden stratospheric warming involving the interaction between the mean (zonally averaged) flow and a single zonal harmonic of wavenumber 1 which is forced at the lower boundary; presumably the tropopause level. In the second experiment the model includes an additional wave 2 which is not forced at the lower boundary but generated through nonlinear interaction between wave 1 and itself. This wave 2 interacts with both the mean flow and wave 1. However, zonal wavenumbers higher than 2 are all neglected. These two experiments are referred to as the linear and the nonlinear cases, respectively. The results are first described in an Eulerian framework. It is found that the simulated warming for the nonlinear case is more intense and rapid than that for the linear case. In order to describe how the different wave components change the mean flow, the transformed equations for the zonally averaged fields of Andrews and McIntyre (1976) are studied diagnostically. Evidence based on the model results is presented to show that the transformed equations provide a more direct view of the wave-forcing processes than the conventional equations. The results of this diagnostic study indicate that, in the nonlinear model experiment, the mean zonal deceleration induced by wave 2 is ∼60% of that induced by wave 1 during the rapid warming stage. The Lagrangian air motions during the two model experiments are described by tracing a large number of marked particles. The format of presentation is the same as that used by Hsu (1980) who discusses the three-dimensional air motions during a simulated warming involving wavenumber 2. It is shown that the particle motions during the model simulation involving a single zonal wave (either wavenumber 1 or 2) are qualitatively similar. In the nonlinear model experiment which includes both waves 1 and 2 and their interactions, the vertical displacements of particles are larger in magnitude and the mixing of polar and tropical air occurs faster, as compared with those in the linear model which involves only wavenumber 1; consistent with the fact that the simulated warming is more intense for the nonlinear model experiment.