  The efficiency of tidal-stream turbines in a large array depends on the
balance between negative effects of turbine-wake interactions and positive
effects of bypass-flow acceleration due to local blockage, both of which are
functions of the layout of turbines. Here we investigate the hydrodynamics of
turbines in an infinitely large array with aligned or staggered layouts for a
range of streamwise and lateral turbine spacing. First, we present a
theoretical analysis based on an extension of the Linear Momentum Actuator Disc
Theory (LMADT) for perfectly aligned and staggered layouts, employing a hybrid
inviscid-viscous approach to account for the local blockage effect within each
turbine row and the viscous (turbulent) wake mixing behind each row in a
coupled manner. We perform Large-Eddy Simulation (LES) of open-channel flow for
28 layouts of tidal turbines using an Actuator-Line Method with periodic
boundary conditions. Both theoretical and LES results show that the efficiency
of turbines (or the power of turbines for a given bulk velocity) in an aligned
array decreases as we reduce the streamwise spacing, whereas that in a
staggered array remains high and may even increase due to the positive local
blockage effect (causing the local flow velocity upstream of each turbine to
exceed the bulk velocity) if the lateral turbine spacing is sufficiently small.
The LES results further reveal that the amplitude of wake meandering tends to
decrease as we reduce the lateral spacing, which leads to a lower wake recovery
rate in the near-wake region. These results will help to understand and improve
the efficiency of tidal turbines in future large arrays, even though the
performance of real tidal arrays may depend not only on turbine-to-turbine
interactions but also on macro-scale interactions between the array and natural
tidal currents, the latter of which are outside the scope of this study.
