Studies of wave-mean interaction relevant to the middle atmospheric circulation

• Main Author: Mo, Ruping
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: University of Cambridge 1994
• Subjects: Wave-mean interaction; Middle atmosphere; Middle atmospheric circulation; Rossby waves; Tuck; polar night
• Online Access: https://www.repository.cam.ac.uk/handle/1810/332681; https://doi.org/10.17863/CAM.80126

The work described in this thesis can be divided into two parts. In the first part (Chapters 2 and 3) we demonstrate how the wave-induced mean motion can be described in terms of the dynamics of Rossby-Ertel potential vorticity (PV). In the second part (Chapters 4 and 5), Rossby waves and their mean effects in the middle atmosphere are investigated within the framework of quasi-geostrophic theory. Chapter 2 describes a simple thought experiment to highlight the usefulness of the description of wave-mean interactions in terms of wave-induced transport of PV-substance (PVS). It is shown that the wave-induced irreversible PVS-transport depends crucially on wave dissipation. When the irreversibility principle for the mean PV anomaly field applies from a coarse-grained perspective, the resulting balanced mean motions are dissipation-dependent, and are equivalent to the O(a$^{2}$) dissipation-dependent mean motions deduced from the momentum viewpoint (a is a dimensionless amplitude parameter). When the invertibility parameter applies from a fine-grain perspective, the balanced mean motions include also the O(a$^{2}$) mean motions induced by the effect of wave transience. In addition, the O(a$^{2}$) dissipation-dependent mean motions are cumulatively much larger than the O(a$^{2}$) dissipation-independent mean motions as time goes on. Thus, even from a coarse-grain perspective, the PV description can provide a key to understanding and characterizing the general character of wave-induced mean motions. Some general relationships between the wave-induced PVS transport and momentum transport are derived in Chapter 3. It is shown that the wave-induced contribution to the PVS transport is closely related to the rate of dissipation of quasimomentum. This result generalizes Taylor's well-known identity, which was derived for a two-dimensional, incompressible, non-rotating fluid (Taylor, 1915), to a stably stratified, rapidly rotating fluid. It also provides a physical basis for the description of wave-induced mean motions in terms of PVS transport. Chapter 4 focuses on the dissipative nature of the Rossby waves and their mean effects in a Charney-Drazin model. It is shown that dissipative processes in the atmosphere not only act to damp the wave amplitude, but also affect significantly the wave phase structure. Moreover, our results suggest that the existence of anomalously-signed (positive) Eliassen-Palm (EP) flux divergences in the middle atmosphere may be physically possible, and the difference between the $\textit{transformed Eulerian mean}$ and the $\textit{generalized Lagrangian-mean}$ meridional circulation is not always negligible. A sharp-edge model on the polar y-plane is introduced in Chapter 5 to study Rossby waves associated with the polar vortex. Results show that the vortex edge can support both free travelling and forced Rossby waves that have a horizontal structure decaying exponentially away from the vortex edge. When the polar night jet is strong enough, the free travelling Rossby waves with each zonal wavenumber tend to travel eastward with approximately the same zonal angular phase velocity, resembling many aspects of the behaviour of the $\textit{4-day waves}$ observed in the winter stratosphere (Randel and Lait, 1991). Of the waves forced by the topography, only those of planetary scale can exist under the typical parameter conditions of the winter stratosphere. Dependences of the EP flux divergence and the mean meridional circulation in the sharp-edge model are also examined. In particular, our result gives no support to the 'flowing processor' hypothesis (Tuck $\textit{et al.}$, 1992, 1993), which requires a significant transport of chemically perturbed air from within the stratospheric polar vortex to mid-latitudes to explain the observed ozone depletion.