### Abstract

As tidal turbine farms grow they interact with the larger scale flow along a channel by increasing the channel's drag coefficient. This interaction limits a channel's potential to produce power. A 1D model for a tidal channel is combined with a theory for turbines in a channel to show that the tuning of the flow through the turbines and the density of turbines in a channel's cross-section also interact with the larger scale flow, via the drag coefficient, to determine the power available for production. To maximise turbine efficiency, i.e. the power available per turbine, farms must occupy the largest fraction of a channel's cross-section permitted by navigational and environmental constraints. Maximising of power available with these necessarily densely packed farms requires turbines to be tuned for a particular channel and turbine density. The optimal through-flow tuning fraction varies from near 1/3 for small farms occupying a small fraction of the cross-section, to near 1 for large farms occupying most of the cross-section. Consequently, tunings are higher than the optimal through-flow tuning of 1/3 for an isolated turbine from the classic turbine theory. Large optimally tuned farms can realise most of a channel's potential. Optimal tunings are dependent on the number of turbines per row, the number of rows, as well as the channel geometry, the background bottom friction coefficient and the tidal forcing.