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We present parameterisations of the subgrid eddy-eddy and eddy-meanfield interactions in a baroclinic ocean representative of the Antarctic Circumpolar Current. Benchmark direct numerical simulations were undertaken using a quasi-geostrophic spectral spherical harmonic code of maximum zonal and total truncation wavenumber of \(T=252\,\). The eddy-eddy interactions are represented by both stochastic and deterministic parameterisations, with model coefficients determined from the direct numerical simulations truncated back to the large eddy simulation truncation wavenumber \(T_R\) less than \(T\). Coefficients of the deterministic eddy-meanfield model are determined by a new least squares regression method. Truncations were repeated for various \(T_R\), with the dependence of the coefficients on \(T_R\) identified. Kinetic energy spectra from the large eddy simulations using these coefficients agree with the direct numerical simulations.   References K. Bryan and J. L. Lewis. A water mass model of the global ocean. J. Geophys. Res. , 84:2503--2517 (1979). doi:10.1029/JC084iC05p02503 J. S. Frederiksen. Precursors to blocking anomalies: the tangent linear and inverse problems. J. Atmos. Sci. , 55:2419--2436 (1998). 2.0.CO;2">doi:10.1175/1520-0469(1998)055 2.0.CO;2 J. S. Frederiksen. Self-energy closure for inhomogeneous turbulence and subgrid modeling. Entropy , 14:769--799 (2012). doi:10.3390/e14040769 J. S. Frederiksen and S. M. Kepert. Dynamical subgrid-scale parameterizations from direct numerical simulations. J. Atmos. Sci. , 63:3006--3019 (2006). doi:10.1175/JAS3795.1 P. R. Gent and J. C. McWilliams. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr. , 20:150--155 (1990). 2.0.CO;2">doi:10.1175/1520-0485(1990)020 2.0.CO;2 S. M. Griffies, A. Gnanadesikan, K. W. Dixon, J. P. Dunne, R. Gerdes, M. J. Harrison, A. Rosati, J. L. Russell, B. L. Samuels, M. J. Spelman, M. Winton, and R. Zhang. Formulation of an ocean model for global climate simulations. Ocean Science , 1:45--79 (2005). doi:10.5194/os-1-45-2005 V. Kitsios, J. S. Frederiksen, and M. J. Zidikheri. Scaling laws for parameterisations of subgrid eddy-eddy interactions in simulations of oceanic circulations. Ocean Modelling , in print (2013). J. N. Koshyk and K. Hamilton. The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere-stratosphere-mesosphere GCM. J. Atmos. Sci. , 58:329--348 (2001). 2.0.CO;2">doi:10.1175/1520-0469(2001)058 2.0.CO;2 M. H. Redi. Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr. , 12:1154--1158 (1982). 2.0.CO;2">doi:10.1175/1520-0485(1982)012 2.0.CO;2 M. J. Zidikheri and J. S. Frederiksen. Stochastic modelling of unresolved eddy fluxes. Geophysical and Astrophysical Fluid Dynamics , 104:323--348 (2010). doi:10.1080/03091921003694701 M. J. Zidikheri and J. S. Frederiksen. Stochastic subgrid-scale modelling for non-equilibrium geophysical flows. Phil. Trans. Royal Soc. A , 368:145--160 (2010). doi:10.1098/rsta.2009.0192

Subgrid parameterisation of the eddy-meanfield interactions in a baroclinic quasi-geostrophic ocean