  We use well-resolved numerical simulations to study the combined effects of
buoyancy, pressure-driven shear and rotation on the melt rate and morphology of
a layer of pure solid overlying its liquid phase in three dimensions at a
Rayleigh number $Ra = 1.25 \times 10^5$. During thermal convection we find that
the rate of melting of the solid phase varies non-monotonically with the
strength of the imposed shear flow. In the absence of rotation, depending on
whether buoyancy or shear dominates the flow, we observe either domes or ridges
aligned in the direction of the shear flow respectively. Furthermore, we show
that the geometry of the phase boundary has important effects on the magnitude
and evolution of the heat flux in the liquid layer. In the presence of
rotation, the strength of which is characterized by the Rossby number, Ro, we
observe that for Ro = O(1) the mean flow in the interior is perpendicular to
the direction of the constant horizontal applied pressure gradient. As the
magnitude of this pressure gradient increases, the geometry of solid-liquid
interface evolves from the voids characteristic of melting by rotating
convection, to grooves oriented perpendicular or obliquely to the direction of
the pressure gradient.
