Although we often think of solids as immovable…

Although we often think of solids as immovable in the face of flow, the motion of air and water sculpts many parts of our world. One common pattern, seen both on surfaces that melt and those that dissolve into a flow, is called scalloping. Mathematical analysis shows that flat surfaces exposed to a flow that melts or dissolves them unavoidably develop these scallops. The surface becomes rougher as the scallops form, but the instability that drives them only works up to a specific level of roughness. Instead of the scallops becoming deeper and deeper, the flow shifts as the surface changes. Peaks in the surface erode faster than the valleys, which tends to keep the scallops relatively uniform in depth after they’ve formed. Scallops like these are often seen in soluble rocks like limestone or marble as well as in snow and ice. (Image credit: Seattle Times, G. Smith; research credit: P. Claudin et al., L. Ristroph)