In this paper, idealised analytical and numerical models are used to explore the potential for local blockage effects to enhance the performance of turbines in tidal channels. Arrays of turbines modelled using the volume-flux-constrained actuator disc and blade element momentum theories are embedded within one-dimensional analytical and two-dimensional numerical channel domains. The effects of local blockage on the performance of arrays comprising one and five rows of actuator discs and tidal rotors operating in steady and oscillatory channel flow are then examined. In the case of steady flow, numerical results are found to agree very well with the two-scale actuator disc theory of Nishino & Willden . In the case of oscillatory flow, however, numerical results show that the shorter and more highly blocked arrays produce considerably more power than predicted by the one-dimensional two-scale theory. These results support the findings of Bonar et al. , who showed that under certain oscillatory flow conditions, the power produced by a partial-width tidal turbine array can be much greater than predicted by two-scale theory. The departure from theory is most noticeable in the case of five turbine rows, where the two-scale theory predicts that the maximum available power should decrease with increasing local blockage but the numerical model shows the maximum available power to increase. The effects of local blockage are found to be less pronounced for the more realistic tidal rotor than for the highly idealised actuator disc but for both models, the results show that in oscillatory flow, considerably more power is available to the shorter and more highly blocked turbine arrays.