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Tidal stream turbines fixed on the seabed can harness the power of tides at locations where the bathymetry and/or coastal geography result in high kinetic energy levels of the flood and/or neap currents. In large turbine arrays, however, avoiding interactions between upstream turbine wakes and downstream turbine rotors may be hard or impossible, and, therefore, tidal array layouts have to be designed to minimize the power losses caused by these interactions. For the first time, using Navier-Stokes computational fluid dynamics simulations which model the turbines with generalized actuator disks, two sets of flume tank experiments of an isolated turbine and arrays of up to four turbines are analyzed in a thorough and comprehensive fashion to investigate these interactions and the power losses they induce. Very good agreement of simulations and experiments is found in most cases. The key novel finding of this study is the evidence that the flow acceleration between the wakes of two adjacent turbines can be exploited not only to increase the kinetic energy available to a turbine working further downstream in the accelerated flow corridor, but also to reduce the power losses of said turbine due to its rotor interaction with the wake produced by a fourth turbine further upstream. By making use of periodic array simulations, it is also found that there exists an optimal lateral spacing of the two adjacent turbines, which maximizes the power of the downstream turbine with respect to when the two adjacent turbines are absent or further apart. This is accomplished by trading off the amount of flow acceleration between the wakes of the lateral turbines, and the losses due to shear and mixing of the front turbine wake and the wakes of the two lateral turbines. Full article