Emergence of a large scale mean flow in rapidly rotating fluid layers

A remarkable feature of two-dimensional turbulence is the transfer of energy from small to large scales. This process can result in self-organization of the flow into large, coherent structures.  Such structures can be found in the atmosphere and oceans, where the flow can be described as (quasi) two dimensional once the horizontal scales are much larger than the vertical ones.

A minimal model of such geophysical flows is a thin, rapidly rotating layer of fluid, where the Coriolis force and the horizontal pressure-gradient are (almost) balanced.  The model encompasses two opposing limits: one gives 2D Navier-Stokes where the dynamics are long-range, the other is a limit of very rapid rotation where the dynamics become local. We explore the emergent large-scale flow in the latter case. This limit allows us to obtain analytical results for the flow and large-scale fluctuations with very few approximations. Examining the spatial fluxes of potential and kinetic energy, we show that the strong mean flow arrests the transfer of kinetic energy to small scales, resulting in an inhomogeneous state even at small scales.

The analytic results are validated by direct numerical simulations, that in addition reveal some intriguing and (yet) unexplained phenomenon of large-scale symmetry breaking.