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-dimensional kinematical model and a two-dimensional geostrophic model. All of these are process-oriented models in isopycnic coordinates, with diapycnal mixing depending on the gradient Richardson number and mixing rapidly developing in subcritical flows. In the first model an initial subcritical condition is specified and mixing is allowed to redistribute the vertical density flux. In the second model the dynamics is specified ad hoc to simulate a frontal system which leads to subcritical conditions 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 mass and momentum conservation equations. In this last model diapycnal mixing controls the mass conservation equation while the momentum equations consist in cross-stream geostrophic balance. All three models produce mixed regions which probably correspond to some of the fine structure density-depth steps that are observed in geophysical flows. The very simple diagnostic and kinematical models have the merit of providing a clear picture of the physical mechanism that produces the density-depth steps, but the potential complexity of the solution is only appreciated when incorporating the dynamics, such as in the geostrophic model.