Scaling of two-dimensional, miscible, laminar density currents flowing down an incline

The intrinsic scales of a laminar two-dimensional density current, are identified. The current is due to a steady, point buoyancy flux of a conservative agent directed parallel to the sloping bottom into the receiving fluid. The independent dimensionless parameters of the problem are the Rayleigh (Ra) and the Schmidt numbers. It is argued that for high enough Ra the effects of the buoyancy-induced pressure gradient are confined to a region near the source. Away from this region, the flow has a boundary layer character, and the scales for the thickness, velocity and concentration are identified. Similarity solutions, based on these scales, brink out some features not observed in experiments. The discrepancy is attributed to the inadequate length of the experimental tanks.