Instabilities of a Baroclinic, Double Diffusive Frontal Zone

Abstract

The linear theory of double diffusive interleaving is extended to take account of baroclinic effects. This study goes beyond previous studies by including the possibility of modes with nonzero tilt in the alongfront direction, which allows for advection by the baroclinic frontal flow. This requires that the stability equations be solved numerically. The main example is based on observations of interleaving on the lower flank of Meddy Sharon, but a range of parameter values is covered, leading to conclusions that are relevant in a variety of oceanic regimes. The frontal zone is treated as infinitely wide with uniform gradients of temperature, salinity, and alongfront velocity. The stationary, vertically symmetric interleaving mode is shown to have maximum growth rate when its alongfront wavenumber is zero, providing validation for previous studies in which this property was assumed. Besides this, there exist two additional modes of instability: the ageostrophic Eady mode of baroclinic instability and a mode not previously identified. The new mode is oblique (i.e., it tilts in the alongfront direction), vertically asymmetric, and propagating. It is strongly dependent on boundary conditions, and its relevance in the ocean interior is uncertain as a result. Effects of variable diffusivity and buoyancy flux ratio are also considered.