Alcove formation in dissolving cliffs driven by density inversion instability

TL;DR

This study models how density inversion instability causes alcove-shaped features to form in dissolving cliffs, highlighting the role of fluid dynamics and boundary layer behavior in shaping these geological features.

Contribution

It introduces a minimal two-phase physical model explaining alcove formation driven by density inversion instability in dissolving cliffsides.

Findings

Alcoves develop due to faster ceiling dissolution caused by density inversion.

Boundary layer thickness influences whether indentations grow or smooth out.

The critical Rayleigh number predicts the alcove opening area and recession rate.

Abstract

We demonstrate conditions that give rise to cave-like features commonly found in dissolving cliffsides with a minimal two-phase physical model. Alcoves that are wider at the top and tapered at the bottom, with sharp-edged ceilings and sloping floors, are shown to develop on vertical solid surfaces dissolving in aqueous solutions. As evident from descending plumes, sufficiently large indentations evolve into alcoves as a result of the faster dissolution of the ceiling due to a solutal Rayleigh-B\'enard density inversion instability. By contrast, defects of size below the boundary layer thickness set by the critical Rayleigh number smooth out, leading to stable planar interfaces. The ceiling recession rate and the alcove opening area evolution are shown to be given to first order by the critical Rayleigh number. By tracking passive tracers in the fluid phase, we show that the alcoves are shaped by the detachment of the boundary layer flow and the appearance of a pinned vortex at the leading edge of the indentations. The attached boundary layer past the developing alcove is then found to lead to rounding of the other sides and the gradual sloping of the floor.