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Hydrodynamic modelling is an important tool for the development of tidalstream energy projects. Many hydrodynamic models incorporate the effect oftidal turbines through an enhanced bottom drag. In this paper we show thatalthough for coarse grid resolutions (kilometre scale) the resulting forceexerted on the flow agrees well with the theoretical value, the force startsdecreasing with decreasing grid sizes when these become smaller than the lengthscale of the wake recovery. This is because the assumption that the upstreamvelocity can be approximated by the local model velocity, is no longer valid.Using linear momentum actuator disc theory however, we derive a relationshipbetween these two velocities and formulate a correction to the enhanced bottomdrag formulation that consistently applies a force that remains closed to thetheoretical value, for all grid sizes down to the turbine scale. In addition, abetter understanding of the relation between the model, upstream, and actualturbine velocity, as predicted by actuator disc theory, leads to an improvedestimate of the usefully extractable energy. We show how the corrections can beapplied (demonstrated here for the models MIKE 21 and Fluidity) by a simplemodification of the drag coefficient.

A correction to the enhanced bottom drag parameterisation of tidal turbines