  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.
Previous investigations suggest these structures to be associated with
shock-formation in the underlying evolution equations, with the regularizing
Gibbs-Thomson effect required for finite tip curvature. Here, we find 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.
