We present a numerical model for 3D time resolved wake calculations from marine current turbines. Since the wakes are characterised by the shedding of a vortex sheet from the rotor blades, we have constructed the model based around the vorticity transport equations. A vortex sheet may be considered a jump contact discontinuity in tangential velocity with, in inviscid hydrodynamic terms, certain kinematic and dynamic conditions across the sheet. The kinematic condition is that the sheet is a stream surface with zero normal fluid velocity; the dynamic condition is that the pressure is equal on either side of the sheet. The kinematic condition is satisfied at the trailing edge only, via an approximation of the Kutta condition. The shed vorticity is the span-wise derivative of bound circulation, and the trailed vorticity is the time derivative of bound circulation, and is convected downstream from the rotors using a finite volume solution of vorticity transport equations.