A geometric mechanism behind sharp crests and scallops in erosion by dissolution

When water flows over soluble rocks such as limestone, salt or gypsum, the feedback between the topography and the flow can lead to the formation of remarkable patterns. One of the most common is known as scallops, and consists of cups-like concavities surrounded by very sharp crests. They can be found typically on the walls of caves carved by underground rivers. Yet very similar patterns form by melting or sublimation of ice, or by ablation on meteorites. The similarity between these patterns, despite the wide range of materials and hydrodynamic conditions, suggests a common and general mechanism.

By comparing field measurements, numerical models and experiments, we propose a geometric approach to explain the generic emergence of scallops. We first characterize the morphology of scallops found on the walls of a limestone cave, and demonstrate the presence of crests which can be seen as singular structures. Then, we discuss the results of numerical models of interface propagation. They allow us to interpret the appearance of crests and the formation of cellular structures as a direct consequence of the fact that the erosion velocity is always directed along the normal to the interface. Finally, we carry out a simple experiment in which patterns are created by dissolution, on the surface of a block of salt, by a solutal Rayleigh-Bénard instability. In accordance with our model, we report the emergence of a cellular pattern of concavities surrounded by sharp crests, very reminiscent of natural scallops.