Tuning tidal turbines in-concert to maximise farm efficiency

Tuning is essential to maximise the output of turbines extracting power from tidal currents. To realise a large fraction of a narrow channel's potential, rows of turbines not only have to be tuned for a particular tidal channel, they must also be tuned in the presence of all the other rows, i.e. 'tuned in-concert'. The necessity for in-concert tuning to maximise farm efficiency occurs because the tuning of any one row affects a channel's total drag coefficient and hence the flow through all other rows. Surprisingly, in several circumstances the optimal in-concert tunings are the same or almost the same for all rows. Firstly, in both constricted and unconstricted channels, rows with the same turbine density have the same optimal tuning. Secondly, turbine rows in channels with a quasi-steady dynamical balance typically have almost the same optimal in-concert tunings, irrespective of their turbine density or any channel constrictions. Channel constrictions, occupying a large fraction of the cross-section or adding more rows of turbines, also make optimal tunings more uniform between rows. Adding turbines to a cross-section increases a farm's efficiency. However, in a law of diminishing returns for quasi-steady channels, turbine efficiency (the output per turbine) decreases as turbines are added to a cross-section. In contrast, for inertial channels with only moderate constrictions, turbine efficiency increases as turbines are added to a cross-section.