Abstract

Persistent large scale flows in geophysical and astrophysical settings are often sustained by small scale turbulence, rather than the other way around. I will discuss two idealized settings where analytical progress on such mean-flow-turbulence interactions and statistics is possible.   Namely, I will compare and contrast the steady state statistics in two limits of the shallow water quasi-geostrophic equation (absent differential rotation): the limit of infinite deformation radius, corresponding to 2D Navier-Stokes, and that of zero deformation radius, called the asymptotic model. For both, I will present analytical results rooted in the quasi-linear approximation, along with supporting evidence from direct numerical simulations. I will also show some surprising features of the asymptotic model, including the influence of the inverse energy transfer on the direct cascade.