Wakes and higher-order turbulence around circular cylinders of different diameters are investigated using particle image velocimetry measurements. The cylinder Reynolds number (Red) is defined by the depth-averaged velocity, cylinder diameter, and kinematic viscosity. The influence of Red on third-order moment of velocity fluctuations, turbulent kinetic energy (TKE) flux, TKE budget, and turbulent length scales are presented. The intermittency factor (IF) and quadrant analysis around the cylinders are discussed for Red values ranging from 12,600 to 21,000. The energy budget mostly near free surface upstream and near-bed downstream is changed due to Red. Stream-wise and transverse TKE fluxes decreased significantly with Red, but not the vertical flux. Stream-wise skewness changed sign from positive to negative at a certain critical distance downstream, while vertical skewness showed reversed effect with Red. Negative stream-wise skewness and positive vertical skewness indicate the occurrence of ejection events. On the downstream, the production and dissipation rates increased with Red, whereas an opposite trend was observed for dissipation only on the upstream. Increase of Red led to an increase in the Kolmogorov length-scale much higher on the upstream than the downstream, whereas it showed depleting effect on Taylor's length-scale on the upstream and an increasing effect on the downstream. Ejection and sweep events were more prominent in the downstream near the cylinder than upstream with higher values of shear stress on the downstream. The sum of the shear stress contributions of all quadrant events increased consistently with an increase in Red near the cylinder.