Towards the minimization of the spurious diapycnal mixing in sigma-coordinate ocean models

F. Lemarié (UCLA, IGPP), L. Debreu (INRIA, Grenoble) and J.C. McWilliams (UCLA, IGPP)

High-order diffusive advection schemes are now widely used in numerous state-of-the-art ocean models. However, as suggested by (Griffies et al, 2000), the diffusion associated to this type of scheme may be large enough to produce excessive diapycnal mixing. In terrain-following coordinates models like ROMS, a strong horizontal mixing along iso-sigma surfaces can thus lead to spurious diapycnal fluxes of heat and salt (and hence density) when it is applied in regions with sloping isopycnals.

This problem has been recently highlighted in
regions with steep topographic features (Marchesiello et al, 2009).
We are currently attempting to diagnose as accurately as possible the damages done to the stratification due to this additional spurious mixing. In parallel a modified version of the ROMS tracer advection scheme is under consideration in order to restore the adiabatic property of advection. This can be done essentially by rotating the diffusion tensor from the horizontal/vertical directions to the isopycnal/diapycnal directions (Marchesiello et al, 2009).

Up to now a special care has been given to the design of an accurate discretization of the rotated diffusion as well as to the numerical stability analysis of the ROMS time stepping algorithm when the modified scheme is used.