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.
Highlights
Estimation of drag forces acting on aquatic surfaces are of interest in many areas of hydraulic and eco-hydraulic engineering, including the assessment of: friction factor; the initiation and rate of sediment transport; appropriate flow regimes for aquatic plants, invertebrates and other biota; and general flow–structure interaction problems (e.g. Ancey et al 2008; Nikora et al 2012; Dey 2014; Kidanemariam &Drag forces on a bed particle in open-channel flowUhlmann 2017)
The low-frequency spectral peak is associated with high coherence between the streamwise velocity component and the drag force and probably results from the action of very-large-scale motions
We propose that the high-frequency region of the drag force spectra is dominated by the action of pressure gradients in the overlying turbulent flow
Summary
Estimation of drag forces acting on aquatic surfaces are of interest in many areas of hydraulic and eco-hydraulic engineering, including the assessment of: friction factor; the initiation and rate of sediment transport; appropriate flow regimes for aquatic plants, invertebrates and other biota; and general flow–structure interaction problems (e.g. Ancey et al 2008; Nikora et al 2012; Dey 2014; Kidanemariam &Drag forces on a bed particle in open-channel flowUhlmann 2017). Estimation of drag forces acting on aquatic surfaces are of interest in many areas of hydraulic and eco-hydraulic engineering, including the assessment of: friction factor; the initiation and rate of sediment transport; appropriate flow regimes for aquatic plants, invertebrates and other biota; and general flow–structure interaction problems This paper will focus on the assessment of drag force fluctuations acting on stationary bed roughness elements. Such considerations are important in order to refine bulk approaches to estimating sediment transport conditions such as threshold Shields parameter (Shields 1936) and include more information about the natural variability of roughness elements and the turbulent velocity field. The surface stresses are related to the velocity field according to the mass and momentum conservation equations supplemented with appropriate boundary conditions. The standard approach is to present the instantaneous drag force (F) proportional to squared velocity as
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