Baroclinic instability of an idealized tidal mixing front

Tidal mixing fronts separate vertically homogenized waters from stratified ambient waters. The linear and nonlinear baroclinic stability of an idealized tidal mixing front is treated here in the parameter range that is stable with regard to symmetric instabilities and that has no bottom friction. All model configurations considered are unstable, and the dependence on bottom slope, stratification and other parameters is similar to that suggested by models (such as that of Blumsack and Gierasch, 1972) with much simpler configurations. The finite-amplitude evolution of the instabilities is treated using a primitive equation numerical model. The initial length scale and growth rate of the instabilities are well predicted by the linear calculations. As the system evolves, gravitational potential energy is transferred to eddy kinetic energy, which peaks at about the time that potential energy stops decreasing. The peak eddy kinetic energy depends strongly on the bottom slope, with the greatest values occurring when the bottom and near-bottom isopycnals slope in the same direction. As the fields continue to evolve, eddy kinetic energy decreases, mean kinetic energy increases, and the eddies become larger and more barotropic. The horizontal eddy mixing coefficient is estimated at the time of maximum lateral heat flux and is found to be sensitive to the magnitude of the bottom slope but not its sign. Overall, the instability and the related eddy mixing are strong enough to encourage the idea that these instabilities might be effective at a more realistic tidal mixing front.