Three-dimensional incompressible Reynolds-Averaged Navier–Stokes (RANS) computations are performed of water flow past an array of tidal turbines, modelled as actuator disks. While recent analytical models provide useful insight into the limit of power extraction and efficiency of tidal turbine arrays, they assume that the turbines are operated uniformly across the entire array. This study presents results of tuning operating conditions across arrays of four and eight turbines, and also the effect of staggering an array of turbines into upstream and downstream sub-arrays. The results show that the power coefficient of a non-staggered array of turbines is maximised when the turbines are operated with a uniform local resistance coefficient across the entire array. This operating condition results in a non-uniform distribution of thrust and power coefficient across the array. For the staggered array, it is found that for a given streamwise separation of sub-arrays the power coefficient is maximised by differential tuning of the front and rear rows, but that the maximum power coefficient does not exceed that achieved by the equivalent non-staggered array. Additionally, for a given efficiency of extraction, i.e., the power extracted by the turbines relative to the total power removed from the flow, the non-staggered array is shown to have a higher power coefficient than the staggered arrays.