MODELING OF SHEAR-INDUCED DIAPYCNAL MIXING IN FRONTAL SYSTEMS

Three shear-induced mixing models are examined and applied to oceanic frontal systems. These are a simple diagnostic model, a one-dimensiona l kinematical model and a two-dimensional geostrophic model. All of th ese are process-oriented models in isopycnic coordinates, with daipycn al mixing depending on the gradient Richardson number and mixing rapid ly developing in subcritical flows. In the first model an initial subc ritical condition is specified and mixing is allowed to redistribute t he vertical density flux. In the second model the dynamics is specifie d ad hoc to simulate a frontal system which leads to subcritical condi tions and we are left to solve the mass conservation equation. In the final model a two-dimensional density-depth field is forced through an externally imposed deformation velocity field and we solve both the m ass and momentum conservation equations. In this last model diapycnal mixing controls the mass conservation equation while the momentum equa tions consist in cross-stream geostrophic balance. All three models pr oduce mixed regions which probably correspond to some of the fine stru cture density-depth steps that are observed in geophysical flows. The very simple diagnostic and kinematical models have the merit of provid ing a clear picture of the physical mechanism that produces the densit y-depth steps, but the potential complexity of the solution is only ap preciated when incorporating the dynamics, such as in the geostrophic model.