A linear stability analysis as well as nonlinear simulations are performed in order
to analyse the coupling between the directional solidification of a binary alloy and
the flow in its melt. An incompressible, potential flow model is assumed, whose
validity is tested through comparisons with the accompanying experiments of Zhang
& Maxworthy (2002) in a Hele-Shaw cell. The linear stability analysis predicts that
a uniform flow parallel to the interface reduces the growth rates of directional
solidification instabilities. In addition, the dominant wavelength is shifted to larger
values by the flow, and a small propagation velocity in the downstream direction is
observed. These findings are confirmed by the nonlinear simulations as well. While
the overall stabilization is confirmed by the experiments, the predicted values of the
dominant wavenumber and its growth rate are too high by factors of two and four,
respectively. These differences are attributed to the existence of a velocity boundary
layer in the melt, which strongly affects the lateral solute transport.