Subgrid modelling for geophysical flows.

Recently developed closure-based and stochastic model approaches to subgrid-scale modelling of eddy interactions are reviewed. It is shown how statistical dynamical closure models can be used to self-consistently calculate the eddy damping and stochastic backscatter parameters, required in large eddy simulations (LESs), from higher resolution simulations. A closely related direct stochastic modelling scheme that is more generally applicable to complex models is then described and applied to LESs of quasi-geostrophic turbulence of the atmosphere and oceans. The fundamental differences between atmospheric and oceanic LESs, which are related to the difference in the deformation scales in the two classes of flows, are discussed. It is noted that a stochastic approach may be crucial when baroclinic instability is inadequately resolved. Finally, inhomogeneous closure theory is applied to the complex problem of flow over topography; it is shown that it can be used to understand the successes and limitations of currently used heuristic schemes and to provide a basis for further developments in the future.

Stochastic subgrid-scale modelling for non-equilibrium geophysical flows.

Methods motivated by non-equilibrium statistical mechanics of turbulence are applied to solve an important practical problem in geophysical fluid dynamics, namely the parametrization of subgrid-scale eddies needed in large-eddy simulations (LESs). A direct stochastic modelling scheme that is closely related to techniques based on statistical closure theories, but which is more generally applicable to complex models, is employed. Here, we parametrize the effects of baroclinically unstable subgrid-scale eddies in idealized flows with broad similarities to the Antarctic Circumpolar Current of the Southern Ocean. The subgrid model represents the effects of the unresolved eddies through a generalized Langevin equation. The subgrid dissipation and stochastic forcing covariance matrices as well as the mean subgrid forcing required by the LES model are obtained from the statistics of a high resolution direct numerical simulation (DNS). We show that employing these parametrizations leads to LES in close agreement with DNS.