Numerical simulations are used to explore the potential for local blockage effects and dynamic tuning strategies to enhance the performance of turbines in tidal channels. Full- and partial-width arrays of turbines, modelled using the volume-flux-constrained actuator disc and blade element momentum theories, are embedded within a two-dimensional channel with a naturally low ratio of drag to inertial forces. For steady flow, the local blockage effect observed by varying the cross-stream spacing between the turbines is found to agree very well with the predictions of the two-scale actuator disc theory of Nishino and Willden (2012, J. Fluid Mech., 708: 596–606). For oscillatory flow, however, results show that, consistent with the findings of Bonar et al. (2019, J. Fluid Mech., 865: 790–810), the shorter and more highly blocked arrays produce considerably more power than predicted by two-scale theory. Results also show that, consistent with the findings of Vennell (2016, Proc. R. Soc. A, 472: 20160047), the ‘dynamic’ tuning strategy, in which the tuning of the turbines is varied over the tidal cycle, can only produce significantly more power than a temporally fixed tuning if the array has a large number of turbine rows or a large local blockage ratio. For all cases considered, trends are consistent between the two turbine representations, but the effects of local blockage and dynamic tuning are found to be much less significant for the more realistic tidal rotor than for the idealised actuator disc.