We consider the solidification of a binary alloy in a mushy layer subject to Coriolis effects. A near-eutectic approximation and large far-field temperature is employed in order to study the dynamics of the mushy layer with a Stefan number of unit order of magnitude. The weak nonlinear theory is used to investigate analytically the Coriolis effect in a rotating mushy layer for a new moderate time scale proposed by the author. It is found that increasing the Taylor number favoured the forward bifurcation.