Double-diffusive transport in laboratory thermohaline staircases

Laboratory experiments were conducted on a double-diffusing fluid stabilized by the faster diffuser (T) and destabilized by the slower diffuser (S), the arrangement that leads to salt fingering. The experiments were conducted in three tanks of depths 2 m, 1 m or 0.3 m, with initial linear profiles of S and T between two reservoirs at fixed or known values, S-0 + DeltaS, T-0 + DeltaT in the top reservoir, S-0, T-0 in the bottom reservoir. In the thermohaline staircase regime consisting of an alternating stack of convecting layers and finger layers, the overall fluxes F-S and F-T are clearly not depth independent. The overall Nusselt number, N-S varies inversely with the number n of finger layers plus convecting layers occurring in the experimental fluid. The largest Nusselt number occurs for n = 1. The number n increases with increasing mean vertical gradient, up to a point. If the vertical gradients are large, n is always equal to 1. Internal measurements show that in the Rayleigh number range \R-S\ similar to 10(15) and density ratio ran e Rrho similar to 1.1 to 1.2, the finger flux F-S(f) similar to (deltaS/h)(RSRrhob)-R-a with a = 0.18 to 0.19 and b = 1.8 to 2.1. The data show dependence of F-S(f) on finger layer thickness h. S In the convecting layers, N-S(e) proportional to R-0.21 for large enough aspect ratio.