Double-Diffusive Intrusions in a Stable Salinity Gradient “Heated from Below”

Abstract

Two-dimensional direct numerical simulations (DNS) are used to investigate the growth and nonlinear equilibration of spatially periodic double-diffusive intrusion for negative vertical temperature Tz < 0 and salinity Sz < 0 gradients, which are initially stable to small-scale double diffusion. The horizontal temperature Tx and salinity Sx gradients are assumed to be uniform, density compensated, and unbounded. The weakly sloping intrusion is represented as a mean lateral flow in a square computational box tilted with a slope equal to that of the fastest-growing linear theory mode; the vertical (?) domain size of the box L*? is a multiple of the fastest-growing wavelength. Solutions for the fastest-growing wavelength show that the intrusion growth is disrupted by salt fingers that develop when the rotation of the isotherms and isohalines by the intrusion shear results in temperature and salinity inversions; the thick inversion regions are separated by a thin interface supporting diffusive convection. These equilibrium solutions were always unstable to longer vertical wavelengths arising because of the merging of the inversion layers. The DNS predicts the following testable results for the maximum lateral velocity U* max = 0.13NSL*?, the lateral heat flux F* = 0.008?CP(Sx/Sz)1/2(NS/KT)1/4NSL*?2.5(?Sz/α), and the interface thickness h? = 0.12L*?, where NS = , g is the gravity acceleration, ? is the density, ?/α is the haline contraction/heat expansion coefficient, and CP is the specific heat capacity. The results are compared with observations in the Arctic Ocean.