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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, $S_0 + \Delta S, T_0 + \Delta T$ 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 $|R_S|\sim 10^{15}$ and density ratio range $R_{\rho}\sim 1.1$ to 1.2, the finger flux $F^f_S\sim {(\delta S/h)}R_S^a R_{\rho}^b$ with $a = 0.18$ to 0.19 and $b = 1.8$ to 2.1. The data show dependence of $F^f_S$ on finger layer thickness $h$. In the convecting layers, $N^c_S \propto R^{0.21}$ for large enough aspect ratio.


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Double-diffusive transport in laboratory thermohaline staircases



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