The formation of Taylor-Görtler vortices inside a melt, driven by a rotating magnetic field, is an intrinsic phenomenon occurring at supercritical Taylor numbers. In this work we numerically study their impact on the macrosegregation and the shape of the mushy zone during unidirectional solidification of Al-7wt-%Si alloy. The weakly turbulent flow was modelled by means of direct numerical simulations in an axisymmetric approach, where the transient heat and mass transfer were simulated by means of a standard mixture model. Both types of solidification, columnar and equiaxed, were considered by the application of both a permeability and a hybrid model to treat the fluid flow in the mushy zone. Our results demonstrate that in the case of columnar solidification the Taylor-Görtler vortices cause both a wavy shape of the mushy zone and segregations in the form of a fir tree with a distinct accumulation of silicon along the axis of the cylinder.