Direct Statistical Simulation of Stochastically-Driven Jets

Abstract:

Statistics of models of geophysical fluids may be directly accessed by solving the equations of motion for the statistics themselves as proposed by Lorenz 50 years ago. Such Direct Statistical Simulation (DSS) is applied to idealized barotropic jets that are driven stochastically. Low-order zonally-averaged statistics are captured by expansions in equal-time cumulants. In the limit of large time-scale separation between the zonal modes and the eddies, the dynamics are quasi-linear, emergent zonal jets are driven directly by the Reynolds stresses exerted by the eddies, and the equations of motion for the cumulants close at second order. We demonstrate that higher-order statistics may also be obtained in this limit through the use of large deviation theory to calculate the rate function of the zonally-averaged Reynolds stress. For moderate separation in time-scales, eddy-eddy interactions must be retained, and cumulant expansions truncated at third order are able to accurately reproduce zonal means and two-point correlations. An alternative closure based upon scale separation is also illustrated.