A study of wave-wave interactions in a steady-state stratospheric model /

Abstract

Interactions among stationary planetary waves in the winter stratosphere are studied using steady-state quasi-geostrophic models from both a theoretical and numerical point of view.A triad of small amplitude waves is examined analytically using a constant zonal wind $beta$-plane model in which dissipation is required for the waves to interact. The nature of the modifications to the linear solutions is found to depend both on the propagation characteristics and the zonal wavenumber of the modes.Numerical solutions are determined using a climatological basic state and boundary forcing. The changes to the linear structure are relatively weak. Zonal wavenumber 1 is the most affected, experiencing primarily an increase in amplitude in the vicinity of 65$sp circ$N, 26 km. As a direct consequence of the almost linear relationship found to exist between the zonal streamfunction and the zonal potential vorticity in middle and northerly latitudes, the wave-wave interactions are, to a first approximation, dissipation-induced. The presence of weak dissipation in this region implies only weak interactions, which explains the quasi-linear structure of the solutions