Drag forces on a bed particle in open-channel flow: effects of pressure spatial fluctuations and very-large-scale motions

The fluctuating drag forces acting on spherical roughness elements comprising the bed of an open-channel flow have been recorded along with synchronous measurements of the surrounding velocity field using stereoscopic particle image velocimetry. The protrusion of the target particle, equipped with a force sensor, was systematically varied between zero and one-half diameter relative to the hexagonally packed adjacent spheres. Premultiplied spectra of drag force fluctuations were found to have bimodal shapes with a low-frequency (${\approx}0.5~\text{Hz}$) peak corresponding to the presence of very-large-scale motions (VLSMs) in the turbulent flow. The high-frequency ($\gtrapprox 4~\text{Hz}$) region of the drag force spectra cannot be explained by velocity time series extracted from points around the particle, but instead appears to be dominated by the action of pressure gradients in the overlying flow field. For small particle protrusions, this high-frequency region contributes a majority of the drag force variance, while the relative importance of the low-frequency drag force fluctuations increases with increasing protrusion. The amplitude of high-frequency drag force fluctuations is modulated by the VLSMs irrespective of particle protrusion. These results provide some insight into the mechanics of bed particle stability and indicate that the optimum conditions for particle entrainment may occur when a low-pressure region embedded in the high-velocity portion of a VLSM overlays a particle.