The diffusive interface at low stability: the importance of non-linearity and turbulent entrainment

Abstract

The diffusion and convection at low temperature at an interface separating a cold, low salinity upper layer from a warmer, more saline lower layer are examined. The densities of the layers are assumed equal and an approximate, non-linear equation of state is used. The vertical transports are determined from the molecular, diffusive fluxes through the interface. The diffusion creates instabilities at the interface, which convect into the layers. The transition from diffusion to convection is estimated from a Rayleigh number based upon the penetration depth of the density anomaly. The convection occurs as quasi-stationary plumes, maintained by inflow of lighter/ denser water, driven by horizontal pressure gradients induced by the density redistribution. The turbulent energy produced in the layers is calculated from the terminal vertical velocity of the buoyant parcels and the horizontal and vertical length scales of the convection. The turbulent energy density is found to depend on layer depth and buoyancy fluxes through the interface cannot be used directly as estimates of the turbulence production. Both turbulent entrainment and the non-linear equation of state could be of less importance for the transport though a diffusive interface in the oceans than what is inferred from corresponding laboratory experiments.