We investigate the near wake of a cylinder at values of Reynolds number corresponding to the onset and development of shear-layer instabilities. By combining quantitative experimental imaging (particle image velocimetry, PIV) and direct numerical simulations at $Re \,{=}\, 3900/4000$ and 10000, we show that the flow structure is notably altered. At higher Reynolds number, the lengths of both the wake bubble and the separating shear layer decrease substantially. Corresponding patterns of velocity fluctuations and Reynolds stress contract towards the base of the cylinder. The elevated values of Reynolds stress at upstream locations in the separated layer indicate earlier onset of shear-layer transition. These features are intimately associated with the details of the shear-layer instability, which leads to small-scale vortices. The simulated signatures of the shear-layer vortices are characterized by a broadband peak at $Re \,{=}\, 3900$ and a broadband high spectral-density ‘plateau’ at $Re \,{=}\, 10\,000$ in the power spectra. The shear-layer frequencies from the present direct numerical simulations study agree well with previous experimentally measured values, and follow the power law suggested by other workers.