Topographic forcing of supercritical convection in a porous medium such as the oceanic crust
Experiments carried out with a Hele-Shaw cell indicate that above the critical Rayleigh number, topography does not control the convection pattern, except when the topographic wavelength is comparable to the depth of water penetration. Scaled to the depth of the layer, the convective wavenumbers are restricted to values between 2.5 and 4.8 - a range that brackets pi, the natural wavenumber for convection in a porous slab with planar, isothermal, impermeable boundaries. Topographies within this range are found to control the circulation pattern perfectly, with downwelling under valleys and upwelling aligned with topographic height. Other topographies do not force the pattern, although it is noted that in some cases the convection wavenumber may be a harmonic of the topographic wavenumber. It is pointed out that unforced circulation cells wander and vary in size because they are not locked to the topography.