Probability Distribution Functions of Velocity Fluctuations and Quadrant Analysis on Turbulent Flow Around a Horizontal Cylinder Across a Channel Bed

An experiment is conducted to investigate the turbulent flow field close to a wall-fastened horizontal cylinder. The evolution of the flow field is analyzed by evaluating turbulent flow characteristics and fluid dynamics along the lengthwise direction. The approach flow velocity retards in the immediate upstream area of the cylinder. At the crest level of the cylindrical pipe, the turbulence characteristics such as Reynolds stresses and turbulence intensities are attaining their peaks. Gram–Charlier (GC) series-based Hermite polynomials yield probability density functions that better match experimental data than those from Gram–Charlier (GC) series-based exponential distributions, demonstrating the superiority of the Hermite polynomial method. Quadrant analysis reveals that sweeps (Q4) dominate intermediate and free-surface zones, while ejections (Q2) prevail near the bed, both being primary contributors to Reynolds shear stress (RSS). The stress component remains minimal or zero for all events when hole size H≥six. Larger hole sizes (≥five) drastically reduced the stress fraction, approaching zero. The stress fraction was highest near the cylinder, decreasing with distance and eventually plateauing. The study enhances the understanding of flow hydraulics around cylindrical objects in rough-bed natural streams.