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Recent developments in the theory of eddy-mean flow interaction in the atmosphere

Interaction between eddies and mean flows has been one of the central themes of fluid dynamics.  Theories date back to Osborne Reynolds and G.I. Taylor, but a major breakthrough occurred from the 1960s to 80s, in which a connection between the group propagation of waves and their radiation stress on the mean flow was firmly established. In the context of dynamic meteorology (my field), the counter-intuitive, anti-frictional nature of Rossby wave radiation stress came to light, and concepts like the generalized Eliassen-Palm flux and the Transformed Eulerian Mean have since become mainstay diagnostics of the general circulation.

Despite these previous efforts, there remain challenges in both (1) a gap between the theory and data, due largely to the small-amplitude assumption made for the waves in the former and (2) lack of theory for Reynolds stress.  Although neither of these challenges will likely go away anytime soon, I will describe some progresses we made recently in the theory of eddy-mean flow interaction in geostrophic turbulence, where both finite-amplitude Rossby waves and turbulent eddies interact with the zonal-mean flow.