Sculpting with rain

Rain is the masterful sculptor of a wide variety of exokarst features. As the overwhelmingly leading source of pure water at the crests of karst fields, it defines the appearance of their skylines. The interaction of individual raindrop impacts with the topography has been linked for example to the emergence of ornamental-like rillenkarren. The flow of rainwater films arguably plays a decisive role in the shaping of the larger scale as well.

In this contribution, we present a model for the two-dimensional and axisymmetric shape evolution of soluble blocks exposed to rainfall. We describe the thin-film flow in the draining regime and the solute transport therein. We identify several families of solutions: namely, one describing a stationary topography, which descends vertically without being deformed, and another, characterised by an asymptotically self-similar evolution. We compare these behaviours with observations from laboratory experiments and discuss the implications to natural occurrences, such as limestone forests.