Buoyancy-driven dissolution of inclined blocks: Erosion rate and pattern formation

The dissolution of a body into quiescent water leads to density stratifications at the interfaces that drive buoyant flows. Where the stratification is unstable, the flow destabilizes into convective solute plumes. By analogy with the Rayleigh-Bénard instability where concentration replaces temperature, this phenomenon is known as the solutal Rayleigh-Bénard instability. Here we report experiments of the dissolution of inclined rectangular blocks made of salt, caramel, or plaster in aqueous solutions of various concentrations. The solute flows along the block while forming plumes before they detach and sink. This flow along the block organizes the emission of plumes within longitudinal parallel stripes with a well-defined millimeter-scale wavelength. The instability of the flow reflects on the concentration field in the boundary layer, which engraves longitudinal grooves onto the block. These grooves interact with the flow and turn into a paving of three-dimensional, cuplike patterns that grow in size and propagate upstream. These bedforms are reminiscent of the scallop bedforms observed on the walls of cave or icebergs. Whereas the block interface is highly dynamical and evolves through time, it remains flat on the global scale and recedes at a stationary rate. We derive scaling laws for the receding velocity and the pattern genesis at the inclined interface that are based on a concentration boundary layer of constant thickness, which is controlled by the flow instability but where neither the patterns nor the flow along the block play any role. We apply these results to the formation of sublimation patterns.