On modeling the turbulent exchange in buoyancy-driven fronts

Mixing and stirring are important processes in the ocean for reasons ranging from their role in the transport of nutrients and pollutants to longer range problems, such as climate prediction. Our primary objective is to evaluate how such processes are carried out by an ocean general circulation model (OGCM) under different modeling choices (e.g., grid resolution, tracer advection scheme, explicit horizontal Reynolds number Re and turbulence closure). Solutions derived from direct numerical simulations (DNS) and large eddy simulations (LES) serve as benchmarks. We present direct comparisons of numerical results for two types of idealized problems: 1) the lock-exchange (LE), which is a simple small-scale computational setting ideally suited to quantify the temporal evolution of mixing due to a gravity current that is driven by a density difference; and 2) the mixed layer instability (MLI), which is similar to the LE problem in terms of the computational setting, but differs dynamically due to the presence of ambient rotation and a high-aspect domain ratio. Such problems are used to compare the transport and stirring of a passive tracer field carried out by the submesoscale MLI eddies.

The LE results show that mixing is more sensitive to the choice of grid resolution than any other parameter tested here. The smallest deviations from the DNS results are achieved with an intermediate spatial resolution. Mixing is also very sensitive to the value of Re, and the errors increase by a factor of approximately two when this parameter is increased by one order of magnitude. The tracer advection scheme, formed by the combination of a third-order upstream-bias in the horizontal with a splines in the vertical, gives larger deviation (excessive mixing) from the DNS results when compared to the multidimensional positive definite advection transport algorithm (MPDATA).

From the MLI results, we find that the transport and stirring of a passive tracer field is very sensitive to the choice of turbulence closure. The best results, with respect to the LES counterpart, are achieved with a combination of k-epsilon and Canuto-A stability functions. Errors increase by a factor of approximately four when the simpler KPP scheme is selected. On both idealized problems, the results do not converge towards the benchmark as grid resolution is increased.

(Gustavo M. Marques and Tamay M.  Ozgokmen - RSMAS, University of Miami, Miami, FL, United States)