Stochastic subgrid model with scaling laws for oceanic simulations

Stochastic and deterministic subgrid-scale parameterisations are developed for the large eddy simulation (LES) of oceanic flows. Parameterisations are developed for a flow representative of the Antarctic Circumpolar Current (ACC), generated using a spectral quasi-geostrophic code. The subgrid eddy viscosity coefficients are calculated using the approach of [3], whereby a high resolution reference direct numerical simulation (DNS) is truncated back to the LES truncation wavenumber T_R. Two subgrid parameterisations are produced: isotropic, in which the coefficients are only dependent on the total wavenumber (n); and anisotropic, in which the coefficients are also dependent on zonal wavenumbers (m). These LES variants reproduce the kinetic energy spectra of the DNS at various resolutions. Scaling laws are determined representing the isotropic profiles, which make the parameterisations more generally applicable, as they remove the need for a higher resolution reference simulation.