Equilibration of Two-Dimensional Double-Diffusive Intrusions

Abstract

Abstract This paper considers the equilibration of lateral intrusions in a doubly diffusive fluid with uniform unbounded basic-state gradients in temperature and salinity. These are density compensated in the horizontal direction and finger favorable in the vertical direction. Previous nonlinear studies of this effect have qualitative and quantitative limitations because of their fictitious parameterizations of the weak “turbulence” that arises. Here, two-dimensional direct numerical simulations (DNS) that resolve scales from the smallest to the intrusive are used to predict the equilibrium state. This is achieved by numerically tilting the x–z computational box so that the mean intrusion is represented by a mode with no lateral variation, but smaller-scale 2D eddies comparable to the intrusion thickness are resolved. The DNS show that the initial plane wave intrusion evolves to an equilibrium state containing both a salt finger interface and a diffusive interface, surrounded by well-mixed layers. The inversion of the horizontally averaged density in the mixed layer is negligibly small, but the salt finger buoyancy flux produces large transient density inversions that drive the mixed layer convection. For the considered values of horizontal/vertical gradients, the calculations yield small Cox numbers and buoyancy Reynolds numbers [comparable to those measured in staircases during the Caribbean-Sheets and Layers Transects (C-SALT) program]. An important testable result is the time-averaged maximum velocity of the fastest-growing intrusion Umax = 18.0 (Σ*z/Σ*x)+1/2KT(gΘ*z/νKT)1/4. Here Θ*z is the undisturbed vertical temperature gradient in buoyancy units, Σ*z and Σ*x are the corresponding vertical and horizontal salinity gradients, g is the gravity acceleration, and ν and KT are the respective values of the molecular viscosity and heat diffusivity. The paradoxical inverse dependence on the horizontal gradient results from the assumption that the latter is unbounded.