  We study numerically the melting of a horizontal layer of a pure solid above
a convecting layer of its fluid rotating about the vertical axis. In the
rotating regime studied here, with Rayleigh numbers of order $10^7$, convection
takes the form of columnar vortices, the number and size of which depend upon
the Ekman and Prandtl numbers, as well as the geometry -- periodic or confined.
As the Ekman and Rayleigh numbers vary, the number and average area of vortices
vary in inverse proportion, becoming thinner and more numerous with decreasing
Ekman number. The vortices transport heat to the phase boundary thereby
controlling its morphology, characterized by the number and size of the voids
formed in the solid, and the overall melt rate, which increases when the lower
boundary is governed by a no-slip rather than a stress-free velocity boundary
condition. Moreover, the number and size of voids formed are relatively
insensitive to the Stefan number, here inversely proportional to the latent
heat of fusion. For small values of the Stefan number, the convection in the
fluid reaches a slowly evolving geostrophic state wherein columnar vortices
transport nearly all the heat from the lower boundary to melt the solid at an
approximately constant rate. In this quasi-steady state, we find that the
Nusselt number, characterizing the heat flux, co-varies with the interfacial
roughness, for all the flow parameters and Stefan numbers considered here. This
confluence of processes should influence the treatment of moving boundary
problems, particularly those in astrophysical and geophysical problems where
rotational effects are important.
