Flows in horizontal thermohaline convection with differential diffusion

Abstract

Oceanographers use the term “differential diffusion” to express a greater value of bulk turbulent diffusivity of temperature within the ocean than the value of bulk diffusivity of salinity, the ratio quantified by Lewis number. Investigation of horizontal thermohaline convection at Prandtl number 1 and infinity over the range reveals a variety of new flow patterns. The chamber has a linearly changing temperature T and salinity S along the top extending from the cold, fresh “polar” end to the hot, salty “tropics” end. It has an aspect ratio of 8 and sides and bottom are insulated and impermeable. Five transition flow patterns occur with little hysteresis for a fixed salinity Rayleigh number Ras of order 105 as Rayleigh number Ra changes from 3.2 × 106 down to 1. They are: 1. A steady T-cell with sinking at the cold end flowing into a bottom flow that feeds up into a top thermal boundary layer. 2. Salty blobs in the boundary layer that amplify and move from the hot to cold end. Each cold end arrival triggers a sudden increase in overturning velocity. 3. A “stripes” pattern where top to bottom cells (alternating T and S cells) move toward the cold end. 4. An S-cell that is a mirror image of the T-cell near the top along with small T-cells lying at the bottom that move toward the cold end 5. A steady S-cell. Each pattern has a distinct volumetric signature in a T-S diagram. Ranges of Ra with various patterns are sizeable at Ras=7.5 × 105 if Le >4/3 but insensitive to Pr. Balanced convection at Ra = Ras >106 adopts a large unsteady supercell containing smaller T and S cells. Exact ranges of the supercell are unknown. Since differential diffusion produces a large collection of flows compared to thermal convection alone, it might produce unexpected new results if added into numerical models of the ocean.