Lagrangian analysis of bed-load sediment motion: database contribution

Abstract

AbstractThe purpose of the present note is to contribute to analysis of bed-load transport processes within a Lagrangian framework. Experiments were performed tracking individual particles under different bed conditions (mobile and fixed beds) at transitional hydrodynamic regimes. A new image processing procedure was designed to obtain the coordinates of each moving sediment within the intermediate range of scales (corresponding to a particle trajectory between rests periods). Thorough attention has been paid to provide consistent definitions for particle motion and trajectory, as well as to devise a rigorous method for analysis. A data set with properties of more than 4000 intermediate trajectories was obtained. Collected data were used to estimate stream-wise and transversal length and duration of intermediate trajectories and corresponding mean sediment velocities. Statistical significance of the values obtained for measured properties was ascertained by appropriate analysis. The full data set is provided with the manuscript as supplementary material.Keywords: Bed-load transportintermediate trajectorieskinematic variablesparticle tracking velocimetrysediment velocity AcknowledgementsThe experimental campaign documented here was performed during an internship of Victoriya Bulankina and Aleksandra Lescova at the Politecnico di Milano. Financial support from the Erasmus scholarship fund of the Riga Technical University is gratefully acknowledged.NotationA = =camera focus area (m2)d = =equivalent sediment diameter (m)g = =acceleration due to gravity (m s−2)H = =duct height (m)Lx = =intermediate trajectory length in stream-wise direction (m)Ly = =intermediate trajectory length in transverse direction (m)N = =number of measurements of u within the logarithmic region (−)n = =sample size (−) = =Shields number (−)Q = =flow discharge (m3 s−1)Qc = =threshold flow discharge for incipient sediment motion (m3 s−1)qs = =sediment transport rate per unit width (−)R = =Reynolds number (−)R* = =grain Reynolds number (−)T = =duration of an intermediate trajectory (s)t = =time (s)ti = =ith instant of time (s)U = =bulk flow velocity (m s−1)u = =time-mean velocity at elevation z (m s−1)u* = =shear velocity (m s−1)ucr* = =critical shear velocity (m s−1)Vx = =stream-wise component of average particle velocity within intermediate trajectory (m s−1)Vy = =transverse component of average particle velocity within intermediate trajectory (m s−1)x = =stream-wise coordinate of particle centroid (m)xti = =stream-wise coordinate of particle centroid at ith instant of time (m)y = =transverse coordinate of particle centroid (m)yti = =transverse coordinate of particle centroid at ith instant of time (m)z = =elevation with respect to the mean sediment level (−)z0 = =virtual origin of the logarithmic flow velocity profile (m)χ2 = =chi-squared distribution (−)Δ = =specific gravity of sediment (−)Δ t = =inverse of the camera acquisition frequency (s)Φ = =dimensionless solid discharge (−)Φf = =dimensionless feeding discharge (−)κ = =von Karman constant (−)μ(Z) = =mean of the generic variable Zρ = =water density (kg m−3)ρg = =sediment density (kg m−3)σ(Z) = =standard deviation of the generic variable Zν"==kinematic viscosity of water (m2 s−1)