The Interaction of Two Internal Waves with the Mean Flow: Implications for the Theory of the Quasi-Biennial Oscillation

TLDR

Internal waves propagating through a dissipative fluid interact with the mean flow, and the underlying dynamics correspond to those described by Holton and Lindzen in their quasi‑biennial oscillation theory. This study elucidates how the period and structure of the resulting oscillation depend on imposed parameters and clarifies the basic dynamics. The authors discuss in detail the origin of the downward motion of shear zones, demonstrating that anomalies in the mean flow structure cannot propagate downward under realistic assumptions. The study finds that a single wave drives the mean flow to a steady state, whereas multiple waves destabilize this state and, with small but nonzero viscosity, generate long‑period oscillations; radiative cooling increases and the mesospheric semi‑annual oscillation are not essential, while lower‑stratosphere momentum diffusion may play a crucial role.

Abstract

Internal waves propagating through a dissipative fluid interact with the mean flow. In response to forcing by a single wave, the mean flow evolves to a steady solution. In the presence of two (or more) waves such a solution exists but is unstable. The underlying dynamics in the latter case are basically those discussed by Holton and Lindzen (1972) in their theory of the quasi-biennial oscillation. If viscosity is small but nonzero the zonal flow exhibits a long-period oscillation. This study elucidates the dependence of the period and structure of the oscillation on the imposed parameters, and clarifies the basic dynamics. In particular, the origin of the downward motion of shear zones is discussed in detail following a demonstration (under realistic assumptions) that anomalies in the mean flow structure cannot propagate downward. Thus it is shown that the increase of radiative cooling coefficient with height in the stratosphere is not crucial to the mechanism while the mesospheric semi-annual oscillation is irrelevant for practical purposes. It is also argued that momentum diffusion in the lower stratosphere may be of crucial importance in the momentum budget of the oscillation.