We present a comprehensive set of two-dimensional (2D) unsteady Reynolds-averaged Navier-Stokes (URANS) simulations of flow around a pair of counter-rotating vertical-axis wind turbines (VAWTs). The simulations are performed for two possible configurations of the counter-rotating VAWT pair, with various gaps between the two turbines, tip-speed-ratios and wind directions, in order to identify key flow mechanisms contributing to the enhanced performance of a pair of turbines compared to an isolated turbine. One of the key mechanisms identified, for the case of two turbines arrayed side-by-side with respect to the incoming wind, is the change of lateral velocity in the upwind path of each turbine due to the presence of the neighbouring turbine, making the direction of local flow approaching the turbine blade more favourable to generate lift and torque. The results also show that the total power of a staggered pair of turbines cannot surpass that of a side-by-side pair of turbines. Some implications of the present results for the prediction of the performance of single and multiple rows (or a farm) of VAWTs are also discussed. The local flow mechanisms identified in the present study are expected to be of great importance when the size of the farm is relatively small. (C) 2016 Elsevier Ltd. All rights reserved.