Instability of an idealized tidal mixing front : symmetric instabilities and frictional effects

Abstract

Finite amplitude instability of an idealized tidal mixing front is considered for cases where there is an active symmetric instability during the early stages of evolution. This can happen either when the initial front is sharp, or when a bottom stress leads to a well-mixed bottom boundary layer under the front. In either case, there is an initial phase, several days long, of slantwise convection, after which a much more energetic and spatially distributed baroclinic or barotropic instability dominates. The presence of an initial symmetrically unstable phase has no obvious effect on the subsequent eddy evolution. Bottom friction does lead to a slower growth rate for baroclinic instabilities, a lower eddy kinetic energy level, and (through stratified spindown) a tendency for flows to be more nearly surface intensified. The surface intensification means that the evolving eddy field cannot proceed toward a barotropic state, and so the horizontal eddy scale is also constrained. Thus, the finite-amplitude inverse cascade is strongly affected by the presence of a bottom stress. Scalings are derived for the frictionally corrected eddy kinetic energy and lateral mixing coefficient. The results, in terms of frictional effects on eddy structure and energy, appear to be valid beyond just the tidal mixing frontal problem.