  Hydrodynamic modelling is an important tool for the development of tidal
stream energy projects. Many hydrodynamic models incorporate the effect of
tidal turbines through an enhanced bottom drag. In this paper we show that
although for coarse grid resolutions (kilometre scale) the resulting force
exerted on the flow agrees well with the theoretical value, the force starts
decreasing with decreasing grid sizes when these become smaller than the length
scale of the wake recovery. This is because the assumption that the upstream
velocity can be approximated by the local model velocity, is no longer valid.
Using linear momentum actuator disc theory however, we derive a relationship
between these two velocities and formulate a correction to the enhanced bottom
drag formulation that consistently applies a force that remains closed to the
theoretical value, for all grid sizes down to the turbine scale. In addition, a
better understanding of the relation between the model, upstream, and actual
turbine velocity, as predicted by actuator disc theory, leads to an improved
estimate of the usefully extractable energy. We show how the corrections can be
applied (demonstrated here for the models MIKE 21 and Fluidity) by a simple
modification of the drag coefficient.
