  We report an idealized numerical study of a melting and freezing solid
adjacent to a turbulent, buoyancy-affected shear flow, in order to improve our
understanding of topography generation by phase changes in the environment. We
use the phase-field method to dynamically couple the heat equation for the
solid with the Navier-Stokes equations for the fluid. We investigate the
evolution of an initially-flat and horizontal solid boundary overlying a
pressure-driven turbulent flow. We assume a linear equation of state for the
fluid and change the sign of the thermal expansion coefficient, such that the
background density stratification is either stable, neutral or unstable. We
find that channels aligned with the direction of the mean flow are generated
spontaneously by phase changes at the fluid-solid interface. Streamwise
vortices in the fluid, the interface topography and the temperature field in
the solid influence each other and adjust until a statistical steady state is
obtained. The crest-to-trough amplitude of the channels are larger than about
10$\delta_{\nu}$ in all cases, with $\delta_{\nu}$ the viscous length scale,
but are much larger and more persistent for an unstable stratification than for
a neutral or stable stratification. This happens because a stable
stratification makes the cool melt fluid buoyant such that it shields the
channel from further melting, whereas an unstable stratification makes the cool
melt fluid sink, inducing further melting by rising hot plumes. The statistics
of flow velocities and melt rates are investigated, and we find that channels
and keels emerging in our simulations do not significantly change the mean drag
coefficient.
