Characteristics of turbulent kinetic energy (TKE) fluxes and budget, conditional Reynolds shear stress (RSS) and Reynolds stress anisotropy in the near- and far-wake flows downstream of a wall-mounted vertical circular cylinder are studied. The TKE fluxes exhibit that the near-wake flow is characterized by an accelerating effect and the far-wake flow by a retarding effect. The TKE budget is explained by using the principle of the TKE conservation. The profiles of TKE budget show that the wall-shear layer of the wall-wake flow is governed by a high negative pressure energy diffusion rate in addition to a high TKE dissipation rate. The conditional statistics of velocity fluctuations were studied to examine the turbulent bursting events by using the quadrant analysis. The conditional RSS profiles illustrate that the near-wake flow is characterized by inward interactions, while the far-wake flow is characterized by sweeps. In the wall-wake flow, the mean duration of bursting events is shorter than their mean interval of occurrence. The Reynolds stress anisotropy reveals that the anisotropic invariant maps appear to be a closed looping trend in the near-wake flow and an open looping trend in the far-wake flow. However, all the profiles, for example, TKE fluxes and budget, conditional RSS and turbulence anisotropy, regain their uninterrupted upstream profiles with an increase in downstream distance. © 2018 Elsevier Masson SAS