Morphological attractors in natural convective dissolution

Ever-changing geological features on this planet never fail to capture our imagination and inspire new scientific advances. Among them, the formation of stone forests is one striking geomorphology caused by dissolution and fluid-structure interactions in nature. Recent experiments demonstrate how a soluble body placed in a fluid spontaneously forms a dissolution pinnacle — a slender, upward pointing shape that resembles naturally occurring karst pinnacles found in stone forests. This unique shape results from the interplay between interface motion and the natural convective flows driven by the descent of relatively heavy solute. In this talk, we will discuss a class of exact solutions that act as attractors for the shape dynamics in two and three dimensions. Intriguingly, the solutions exhibit large but finite tip curvature without any regularization, and they agree remarkably well with experimental measurements. The relationship between the dimensions of the initial shape and the final state of dissolution may offer a principle for estimating the age and environmental conditions of geological structures.