Stochastic subgrid modelling

Self-energy stochastic subgrid modelling in simulations of quasi-geostrophic and boundary layer flows

Abstract

Stochastic models are developed for the subgrid turbulence interactions in simulations of three-dimensional boundary layers, and quasi-geostrophic atmospheres and oceans. In geophysical (and engineering) simulations it is not possible to resolve all scales of motion, so one must resort to large eddy simulation (LES), where the large eddies are resolved on a computational grid and the interactions with the unresolved subgrid scales are arameterised. If these interactions are not self-consistently parameterised, then the results become resolution dependent. This has been a significant and long standing problem since the earliest simulations of weather and climate. In typical approaches one starts with a physical hypothesis that then leads to a subgrid model. In contrast I will present a new stochastic self-energy approach in which the model coefficients are determined from the statistics of high resolution reference simulations, with physical interpretations made apostiori. The subgrid model consists of a meanfield shift, deterministic drain dissipation acting on the resolved field and a stochastic backscatter force. Subsequent LESs adopting these coefficients
reproduce the statistics of the higher resolution simulations across all scales of motion, solving the resolution dependence problem. In addition, as no assumptions are made concerning the form of the subgrid model, further insight into the physics is attained from the properties of the subgrid coefficients concerning the direction, magnitude and stochasticity of the transfer of energy between eddies of varying scale.