Analytical models of the flow passing through a porous actuator disc can be used to estimate the power that can be extracted by a wind or tidal turbine. However, the models that have been developed to date assume that the flow field is uniform upstream of the turbine. In practice this is not the case for both wind and tidal turbines, where a non-uniform sheared velocity profile is more likely. To help overcome this problem, in this paper we extend the traditional actuator disc models to incorporate nonuniform upstream flow. Using the extended model we show that flow non-uniformity alters the power that can be removed by a disc in a confined flow because it alters the 'effective blockage' of the disc. Results from the model compare very well with numerical solution of the Euler equations and have potentially important implications for quantifying blockage effects experienced by wind turbines in tunnels and tidal turbines in tidal channels when the velocity profile is not uniform.
