Parameterizing Entrainment Induced by Submesoscale Eddies

Submesoscale eddies in the ocean surface layer are known to cause the restratification of the mixed-layer by converting the potential energy stored in the outcropping isopycnals into kinetic energy. Evidence of entrainment and subduction is found associated to submesoscale eddies, suggesting their importance for the biogeochemistry of the global ocean. Submesoscale eddies cannot be resolved in today’s global ocean models and existing parameterizations for baroclinic mixed-layer instabilities (MLIs), which are proven to reproduce the restratification quite well, are not capable to fully capture the vertical exchange of passive tracers across the mixed-layer. In this study, high resolution numerical simulations show the inadequacy of the MLI parameterization of Fox-Kemper, Ferrari, and Hallberg (2008, ‘FFH’) for the entrainment problem. A method for tracer inversion is then used to gain insights on the tracer transport in order to inform the parameterization. Parameter dependence is explored by considering different ocean initial conditions. Finally, the results show that a diffusive (symmetric) component needs to be included to the streamfunction (anti-symmetric) to entirely represent the transport induced by MLIs: the parameterization for entrainment is an update to the FFH parameterization.