The influence of an external shear flow on the evolution of a solidifying array of dendritic crystals, termed a mushy layer, is investigated through controlled cooling of an aqueous ammonium chloride solution in a laboratory flume. The controlled cooling produces a mushy layer that grows at a constant rate from the base of the flume over which a laminar shear flow is applied. We find a critical flow speed above which a spatiotemporal variation of the solid fraction of the layer appears with a planform transverse to the flow direction. The presence of this distinctive pattern of spanwise crevasses is compared with a simplified stability analysis in which the motion of the external fluid over the corrugated mush–liquid interface produces a pressure perturbation that drives flow and phase change within the mushy layer. This flow leads to a pattern of solidification and dissolution that is compared to the experimental results. The physical mechanism underlying the pattern formation is confirmed by the agreement between the theoretical predictions and experimental results. Finally, the comparison between theory and experiment provides a value for the mushy layer permeability, the evolution of which is of relevance to a host of geophysical, biological and engineering systems.