Laboratory studies of high Rayleigh number circulation in an open-top Hele-Shaw cell: An analog to mid-ocean ridge hydrothermal systems

Ridge crest hydrothermal systems are generally characterized by high heat fluxes and a permeable top which allows fluids to flow freely across the seafloor. The basic patterns of flow and heat transport in such systems are poorly known especially at high Rayleigh numbers. We present the results of a laboratory study using a wide-aspect ratio, open-top Hele-Shaw cell heated from below. The model is an analog for two-dimensional hydrothermal convection. The onset of convection occurs at a Rayleigh number Ra = 20.4 in good agreement with numerical predictions. Above onset, the spacing of upwelling plumes decreases quickly with the Rayleigh number before reaching an asymptotic limit in the range 0.2-0.3 above Ra approximate to 125. Periodic unsteady flow is first observed at Ra approximate to 47 and is a result of small thermals that are advected horizontally in the bottom boundary layer. The amplitude, frequency, and irregularity of oscillations increase with the Rayleigh number. Unsteadiness can also result from the repeated formation of new plumes accompanied by the merging of plumes elsewhere in the model. Above Ra approximate to 590, the flow patterns show no dominant frequency and are chaotic. In the unsteady regime the frequency of oscillations scales as Ra-1.92 and the Nusselt number scales as Ra-0.91 above Ra approximate to 200. These relationships are in close agreement with theoretical scalings for high Rayleigh number porous convection, Nu a Ra and f proportional to Ra-2. Assuming vigorous mid-ocean ridge systems can be approximated by flow through a Darcy porous media, our results predict that upwelling sites will be spaced at about half the depth of circulation. This is compatible with observations on the Endeavour segment of the Juan de Fuca Ridge. Our results also predict that ridge crest hydrothermal systems with Nusselt numbers of 10-500, will exhibit unsteady flow at periods of similar to 500-0.2 years. Unsteady convection has not yet been observed, perhaps because highly permeable flow channels stabilize the flow in real systems.