Hot-wire measurements were made simultaneously in two homogeneous ‘horizontal’ planes in the far-wake region of a cylinder. A technique developed using hot-wire data to identify the spatial characteristics of the large-scale bulges at the interface between the internal turbulent motions and the external irrotational flow was used to unambiguously relate these outer intermittent bulges to the inner coherent structures. It was found that a turbulent bulge is made up of a combination of a horseshoe vortex (whose legs form one double-roller eddy) and the straining region present just upstream of this structure. The approach also allowed the evaluation of the two most prominent phenomenological models for the entrainment mechanism in the far-wake region: the Kelvin–Helmholtz instability and Townsend's growth–decay cycle. It was found that the decaying and re-forming of the bulges and entrainment structures is not likely to occur. Rather, the evidence is that the large-scale bulges remain coherent for long streamwise distances in equilibrium with the overall similarity of the flow.