  The actuator disk model (ADM) continues to be a popular wind turbine
representation in large eddy simulations (LES) of large wind farms.
Computational restrictions typically limit the number of grid points across the
rotor of each actuator disk and require spatial filtering to smoothly
distribute the applied force distribution on discrete grid points. At typical
grid resolutions, simulations cannot capture all of the vorticity shed behind
the disk and subsequently over-predict power by upwards of 10%. To correct
these modeling errors, we propose a vortex cylinder model to quantify the shed
vorticity when a filtered force distribution is applied at the actuator disk.
This model is then used to derive a correction factor for numerical simulations
that collapses the power curve for simulations at various filter widths and
grid resolutions onto the curve obtained using axial momentum theory. The
proposed correction therefore facilitates accurate power measurements in LES
without resorting to highly refined numerical grids.
