Effects of mesoscale eddies in the active mixed layer: test of the parametrisation in eddy resolving simulations

Abstract

In eddy resolving simulations, we test a mixed layer mesoscale parametrisation, developed recently by Canuto and Dubovikov [Ocean Model., 2011, 39, 200–207]. With no adjustable parameters, the parametrisation yields the horizontal and vertical mesoscale fluxes in terms of coarse-resolution fields and eddy kinetic energy (EKE). We compare terms of the parametrisation diagnosed from coarse-grained fields with the eddy mesoscale fluxes diagnosed directly from the high resolution model. An expression for the EKE in terms of mean fields has also been found to get a closed parametrisation in terms of the mean fields only. In 40 numerical experiments we simulated two types of flows: idealised flows driven by baroclinic instabilities only, and more realistic flows, driven by wind and surface fluxes as well as by inflow-outflow. The diagnosed quasi-instantaneous horizontal and vertical mesoscale buoyancy fluxes (averaged over $1^{\circ }$ – $2^{\circ }$ and 10 days) demonstrate a strong scatter typical for turbulent flows, however, the fluxes are positively correlated with the parametrisation with higher ($0.5-0.74$) correlations at the experiments with larger baroclinic radius Rossby. After being averaged over 3–4 months, diffusivities diagnosed from the eddy resolving simulations are consistent with the parametrisation for a broad range of parameters. Diagnosed vertical mesoscale fluxes restratify mixed layer and are in a good agreement with the parametrisation unless vertical turbulent mixing in the upper layer becomes strong enough in comparison with mesoscale advection. In the latter case, numerical simulations demonstrate that the deviation of the fluxes from the parametrisation is controlled by dimensionless parameter estimating the ratio of vertical turbulent mixing term to mesoscale advection. An analysis using a modified $\mathit{\omega }$-equation reveals that the effects of the vertical mixing of vorticity is responsible for the two–three fold amplification of vertical mesoscale flux. Possible physical mechanisms, responsible for the amplification of vertical mesoscale flux are discussed.

Keywords:

• Mesoscale parametrisation
• Active mixed layer
• Eddy resolving simulations
• Restratification
• Eddy diffusivity
• $\mathit{\omega }$-equation

Acknowledgements

The work has been dedicated to Professor John Huthnance on the occasion of his retirement. We thank Professor V.M. Canuto for a useful discussion of the manuscript and an anonymous reviewers for detailed analysis of our paper and valuable criticisms. The authors acknowledge the National Capability funding provided by the UK Natural Environment Research Council (NERC), the Office of Naval Research under grants N00014-03-1-0989 and N00014-12-10188, and the NASA High-End Computing (HEC) Program through the NASA Center for Climate Simulation (NCCS) at the Goddard Space Flight Center.

Notes

No potential conflict of interest was reported by the authors.