  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.
