  The performance and economics of turbines in a tidal array are largely
dependent on the power per turbine, and so approaches that can increase this
power are crucial for the development of tidal energy. In this paper, we
combine a two-scale partial array model and a one-dimensional channel model to
investigate the effects of blockage, turbine arrangement, and channel dynamics
on tidal turbines. The power per turbine is obtained as the product of two
parameters: a power coefficient measuring the power acquired from the
instantaneous flow and an environment coefficient showing the response of the
channel to added drag. The results suggest that taking account of channel
dynamics will decrease the predicted power and the optimal induction factor.
The model also shows that when the number of turbines in a row is increased,
the power per turbine may monotonically increase or decrease or attain a
maximum value at a certain global blockage. These different results depend on
two characteristic parameters of the channel: $\alpha$ and $\lambda_D$.
Furthermore, we find that besides turbine density (blockage), the arrangement
of the turbines should also be considered if we want to obtain an efficient
array. Appropriate arrangements can enhance the performance of turbines in
tidal channels, although the beneficial effects will be partly offset by
reduced velocities. The turbine arrangement also has an effect on the optimal
global blockage at which the power attains its maximum value. As the rate of
increase of the power per turbine from an array spanning the whole channel
width to the optimal partial array diminishes with increasing blockage, the
optimal global blockage will also decrease.
