A vertically stable density stratification with temperature gradient Tz < 0, salinity gradient Sz < 0, and with density compensating horizontal T/S gradients is unstable to lateral intrusions because the molecular heat diffusivity is much larger than the salt diffusivity. Previous marginal instability theory is extended to the supercritical regime. The fastest growing vertical wavelength (δz) is obtained in a model of a T/S front with finite lateral width (L*) and lateral salinity variation (ΔS). The value of δz ≈ ΔS/|Sz| varies only slightly with the parameters, and this result is applied to the smallest "step" size observed in the main thermocline of the Weddell Sea. Nonlinear considerations show that the laterally divergent heat/salt flux produced by the instability forces a mean vertical circulation which enhances the compensating lateral T/S gradients, thereby accelerating the intrusive instability, and eventually producing local density ratios sufficient to initiate strong vertical convection. This suggests that weak isopycnal T/S gradients are necessary to initiate the steps which subsequently merge into larger layers.
Stern, Melvin E.. 2003. "Initiation of a doubly diffusive convection in a stable halocline." Journal of Marine Research 61, (2). https://elischolar.library.yale.edu/journal_of_marine_research/8