Stochastic Subgrid Turbulence Parameterisation of Eddy-Eddy, Eddy-Meanfield, Eddy-Topographic and Meanfield-Meanfield Interactions in the Atmosphere

Stochastic subgrid turbulence parameterisations are developed for a baroclinic quasi-geostropic (QG) atmosphere with a January background state and realistic topography. The parameterisation coefficients are calculated from the statistics of higher resolution reference direct numerical simulations (DNS). Separate parameterisations are developed for each of the fundamental subgrid interactions. The first are the transient eddy-eddy interactions, which are between subgrid and resolved eddies. The second are the eddy-meanfield interactions between the subgrid eddies and the resolved meanfield. The third are the meanfield-meanfield interactions between the resolved meanfield and topography and their unresolved counterparts. Finally the eddy-topographic interactions are between the subgrid eddies and the resolved topography. This parameterisation framework is validated by producing large eddy simulations (LES) of the atmosphere that agree with the reference DNS. As compared to the DNS of truncation wavenumber 63, successful LES are produced with a truncation wavenumber of 15, using only 1.3% of the computational effort. This is particularly impressive as it captures both the drain of energy out of the system due to the forward enstrophy cascade, and the injection of energy associated with the unresolved baroclinic instability.