Abstract

This study concerns the behaviour of reduced models for turbulence--mean-flow interactions. In modelling, an idealised sea of random waves or turbulent eddies is usually driven by a stochastic body force. However the stochasticity of the zonal mean flow is often neglected, following an ergodic assumption that the zonal mean is equal to the ensemble mean. In this study, we examine the stochasticity of the zonal mean flow and its consequences for zonostrophic instability, which accounts for the spontaneous generation of zonal flows observed in many planetary and geophysical fluid systems . From large numbers of realisations of an idealised fluid system, we show that  the zonal mean flow typically exhibits considerable stochasticity.  We further examine the correlation between waves and mean flows, and demonstrate its impact on the growth rate of the instability. Theoretical predictions are verified by numerical simulations.