A parameter sweep experiment on quasi-periodic variations of the polar vortex due to wave-wave interaction in a barotropic model

Quasi-periodic variations of the winter polar vortex in the Southern Hemisphere are characterized by the wave-wave interaction between quasi-stationary planetary wave of zonal wavenumber 1 (Wave 1) and eastward traveling Wave 2 as studied by Hio and Yoden (2004; JAS). In that paper we showed an example of periodic solution of a barotropic model in which stationary Wave 1 forced by surface topography interacts with eastward traveling Wave 2 generated by the barotropic instability of a forced zonal mean zonal flow.

In the same barotropic model with zonal-flow forcing, dissipation, and surface topography, several types of time-dependent solutions, such as stationary-wave solution, periodic solution, quasi-periodic vacillation solution, and irregular non-periodic solution, are obtained for the combination of external parameters of the height of sinusoidal surface topography and the width of eastward zonal jet. Details of the wave-wave interactions are described for the transition from periodic solution for finite amplitude of surface topography to quasi-periodic solution for smaller amplitude of topography. Variations of mean zonal flow and topographically forced Wave 1 synchronize with periodic progression of Wave 2 in the periodic solutions, while variations of mean zonal flow and amplitudes of Waves 1 and 2 are independent of the progression of Wave 2 in the quasi-periodic vacillation. Dominant triad interactions are obtained for each of these solutions.