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

Abstract

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.

Entrainment of sediment particles by very large-scale motions

“…Overall, the indications of figures 1(a) and 1(b) and the analysis of Cameron et al (2019) are that as VLSMs contribute significantly to particle drag forces, they should also directly contribute to particle entrainment, particularly at larger protrusions. This hypothesis will be tested in this study using particle image velocimetry (PIV) recordings of the flow field leading up to, during, and after the instant of the entrainment of single spherical particles.…”

“…Recent experiments (Cameron et al 2019) demonstrated that the pre-multiplied frequency spectrum of drag force fluctuations (f S D , where f is frequency and S D is drag force auto-spectra) acting on spherical bed particles has a bimodal shape, with a low frequency peak corresponding to the presence of very-large-scale motions (VLSMs) in the flow, and a higher frequency peak corresponding to the action of turbulent pressure spatial fluctuations (figure 1a). The low frequency peak in figure 1(a) is sensitive to the particle protrusion (P ) reflecting increased exposure of the particle to the flow.…”

“…The function T Dp acts as a differencing filter reflecting that the drag force is proportional to the pressure difference between upstream and downstream particle faces. Data are not available yet to directly estimate Cameron et al (2019), however, suggest that it is reasonably approximated by…”

The Physics of Sediment Transport Initiation, Cessation, and Entrainment Across Aeolian and Fluvial Environments

“…These authors concluded that such pressure gradient fluctuations must be important also for the mobilization of bed sediment. In fact, numerous laboratory, field, and theoretical studies have advocated the viewpoint that the magnitude of peaks of the instantaneous flow force acting on a bed particle, consisting of both lift and drag forces, is a key aspect of fluid entrainment (e.g., Apperley & Raudkivi, 1989;Cameron et al, 2019Cameron et al, , 2020Dwivedi et al, 2010aDwivedi et al, , 2010bGiménez-Curto & Corniero, 2009;Heathershaw & Thorne, 1985;Hofland et al, 2005;Kalinske, 1947Kalinske, , 1967Kirchner et al, 1990;Nelson et al, 1995;Paintal, 1971;Papanicolaou et al, 2001;Schmeeckle et al, 2007;Sumer et al, 2003;Vollmer & Kleinhans, 2007;Zanke, 2003). However, while such force peaks explain certain observations, such as the episodic character of very weak turbulent bedload transport (Helland-Hansen et al, 1974;Hofland, 2005;Paintal, 1971) or the strong increase of weak turbulent bedload transport in the presence of vegetation (Yang & Nepf, 2018Yager & Schmeeckle, 2013), they do not explain all observations.…”

Inertial drag and lift forces for coarse grains on rough alluvial beds

“…Previous laboratory studies using fixed vibration sensors attached to grains (Schmeeckle et al, 2007;Cameron et al, 2019) report nominal drag and lift forces at the order of magnitude of 0.1 N for 0.008 -0.025 m diameter particles (and for comparable hydraulic conditions to the flume experiments presented here, Appendix B). In the flume results presented here, the inertial drag and lift forces during entrainment are recorded at an order of magnitude of 10 N. This two order of magnitude difference is expected since: a) the particles examined here have a 5x larger (actual or equivalent) average diameter compared to these works, resulting to a mass larger by a factor of 125; and b) the inertial sensor is unrestricted (freely mobile) meaning that the inertia of the moving particle is fully captured.…”