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In this paper we perform Direct Statistical Simulations of a model oftwo-dimensional flow that exhibits a transition from jets to vortices. Themodel employs two-scale Kolmogorov forcing, with energy injected directly intothe zonal mean of the flow. We compare these results with those from DirectNumerical Simulations. For square domains the solution takes the form of jets,but as the aspect ratio is increased a transition to isolated coherent vorticesis found. We find that a truncation at second order in the equal-time butnonlocal cumulants that employs zonal averaging (zonal CE2) is capable ofcapturing the form of the jets for a range of Reynolds numbers as well as thetransition to the vortex state, but, unsurprisingly, is unable to reproduce thecorrelations found for the fully nonlinear (non-zonally symmetric) vortexstate. This result continues the program of promising advances in statisticaltheories of turbulence championed by Kraichnan.

Direct Statistical Simulation of Jets and Vortices in 2D Flows