SMILES DNS Simulations

To further our understanding of the dynamical evolution of mixed layer submesoscale eddies, the SMILES modelling team at the University of Cambridge are currently performing a series of frontal spindown simulations at very high resolution - around 5000 times higher than the resolution used by state of the art global ocean models. These simulations will be run on Cambridge’s supercomputer, Darwin, and are intended to help us understand the interaction between small-scale turbulence and larger submesoscale motions which are constrained by the mixed layer density stratification and the rotation of the earth.

Our direct numerical simulations (DNS) solve the viscous Boussinesq Navier-Stokes equations in a flat-bottom “frontal zone” model. The basic state in this model configuration is an idealization of the upper ocean at a front, where the density varies both vertically and laterally. The lateral density gradient provides a source of available potential energy, and in conjunction with weak vertical stratification permits a variety of dynamical instabilities (e.g. baroclinic, symmetric, Kelvin-Helmholtz) to grow. The time-evolving part of the flow is represented by the departures in velocity and density away from the basic state. These departures are periodic in both horizontal directions, allowing us to use spectral methods. In addition, we enforce no vertical flux and free slip boundary conditions at top and bottom, using central differencing to solve in this direction. Time-stepping is done using a third order, low-storage Runge-Kutta algorithm.

The basic velocity field in each simulation is set to be in thermal wind balance with the lateral density gradient of the front, whose strength is controlled by the choice of an initial gradient Richardson number. The two primary types of fluid instability in these simulations are symmetric and baroclinic instability. Initializing the model with small Richardson number (< 1) allows us to observe the transition between symmetric and baroclinic instabilities that occurs as the flow restratifies, quantify the associated transition of turbulent kinetic energy sources, and resolve the full range of secondary instabilities that are also present at high resolution. None of these features are yet well understood by existing theory.