Double-Diffusive Intrusions on a Finite-Width Thermohaline Front

A density-compensated thermohaline front with a finite width L∗ and total lateral salinity variation ΔS superimposed on a finger-favorable thermocline is studied by means of linear theory and nonlinear numerical calculations using parameterized finger fluxes. By retaining the relatively small molecular heat diffusion and the dependence of the finger Nusselt number Nu on the density ratio, it is shown that marginal stability with critical ΔS is possible. The lateral fluxes induce a mean vertical velocity w0(x), which can sharpen the front, but when ΔS exceeds a certain value the effect of the lateral fluxes exceeds that of w0(x) and the front weakens. Nonlinear 2D spectral calculations showed that the modification of the mean horizontal gradients is small and that the intrusions continue to grow exponentially even after they have produced overturns. By extrapolating the linear theory results beyond the overturning stage, the intrusion velocity was estimated to be proportional to the Brunt–Väisälä frequency multiplied by the intrusion thickness.