Morphological attractors in natural convective dissolution

Abstract

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.

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Cited by in corpus (7)

• Emergence of tip singularities in dissolution patterns
• Predicting convection configurations in coupled fluid-porous systems
• How fluid-mechanical erosion creates anisotropic porous media
• Large-scale circulation reversals explained by pendulum correspondence
• Alcove formation in dissolving cliffs driven by density inversion instability
• Melting of olive oil in immiscible surroundings: experiments and theory
• Dissolution-driven transport in a rotating horizontal cylinder