 Slope-driven porous gravity current

A buoyant phase beneath a sloping impermeable cap has a slope-driven Darcy velocity proportional to density deficit and slope. Far from thickness-adjustment regions, its uniform plateau speed is $K\Delta \rho g\sin \theta /\mu$. With thickness measured normal to the slope, buoyant cap overpressure is $\Delta \rho gh\cos \theta$. A complete depth model also includes the along-current gradient of thickness.