The performance and detailed near-wake characteristics of a vertical axis, cross-flow turbine (CFT) of aspect ratio 1 were measured in a large cross-section towing tank. The near-wake at one turbine diameter downstream was examined using acoustic Doppler velocimetry, where essential features regarding momentum, energy, and vorticity are highlighted. Dominant scales and their relative importance were investigated and compared at various locations in the measurement plane. Estimates for the terms in the mean streamwise momentum and mean kinetic energy equation were computed, showing that the unique mean vertical velocity field of this wake, characterised by counter-rotating swirling motion, contributes significantly more to recovery than the turbulent transport. This result sheds light on previous CFT studies showing relatively fast downstream wake recovery compared to axial-flow turbines. Finally, predictions from a Reynolds-averaged Navier-Stokes simulation with the commonly used actuator disk model were compared with the experimental results, evaluating its use as an engineering tool for studying flow in CFT arrays. Unsurprisingly, the model was not able to predict the near-wake structure accurately. This comparison highlights the need for improved parameterised engineering models to accurately predict the near-wake physics of CFTs.