Topographic forcing of thermal convection in a Hele-Shaw cell model of a porous medium

Topographic forcing of porous convection was investigated by modifying the Hele-Shaw cell to have a sinusoidally contoured, isothermal upper boundary. Eight different topographies with nondimensional wavenumbers between 1.43 and 8.17 were employed. The amplitude of each topography tapers linearly (over a factor of three to six) from one end of the apparatus to the other, and the mean topographic amplitude is 0.05 to 0.08 times the average depth of the layer. These experiments reveal two different flow regimes: subcritical flow occurs when the Rayleigh number is less than the critical Rayleigh number for a layer with flat boundaries, while supercritical flow develops at higher Rayleigh numbers.