Experimental and theoretical study of bed load particle velocity

Unified Model of Sediment Transport Threshold and Rate Across Weak and Intense Subaqueous Bedload, Windblown Sand, and Windblown Snow

“…Coupled DEM/large eddy simulations by Liu et al (2019) of a grain saltating along a fixed quadratically arranged (i.e., idealized) bed driven by water showed a skewed streamwise velocity distribution and, consistently, a substantial difference in the average streamwise grain motion when compared with simulations in which turbulent fluctuations were turned off. In contrast, experiments indicate symmetric Gaussian-like distributions of the streamwise velocity of energetic grains in natural aeolian and fluvial NST along random close packed (i.e., nonidealized) erodible beds (Ancey & Pascal, 2020;Heyman et al, 2016;Kang et al, 2008;Shim & Duan, 2019). We take this as evidence that, for natural conditions, the second requirement is approximately satisfied, though we recognize the potential of making a substantial error when assuming that the fluctuating turbulent flow can be approximated by its mean for modeling the mean motion of energetic grains.…”

“…Note that we are modeling only those grains that have approached a nontrivial steady state trajectory, that is, comparably energetic grains that have survived multiple interactions with the bed surface without being captured. The velocity distribution of such grains would be expected to be Gaussian if their velocity fluctuations were predominantly caused by grain-bed interactions (Ho et al, 2012), while it would be expected to be skewed (e.g., log-normal or exponential) if their velocity fluctuations were predominantly caused by streamwise flow fluctuations (Shim & Duan, 2019) because τ fluc is log-normally distributed (Cheng & Law, 2003;Martin et al, 2013). Coupled DEM/large eddy simulations by Liu et al (2019) of a grain saltating along a fixed quadratically arranged (i.e., idealized) bed driven by water showed a skewed streamwise velocity distribution and, consistently, a substantial difference in the average streamwise grain motion when compared with simulations in which turbulent fluctuations were turned off.…”

On Bed Form Resistance and Bed Load Transport in Vegetated Channels

“…Similarly, bed load transport rate is the product of bed load particle velocity and the thickness of bed load layer [34][35][36][37]. The thickness of bed load layer is defined as the equivalent bed thickness assuming the bed load layer consists of only bed load particles.…”

“…The real thickness of mobile bed load layer is greater than this value due to the porosity of bed material. Shim and Duan [37] conducted a series of laboratory experiments using highspeed camera to measure bed load particle velocity, and found the spatial and temporal averaged bed load particle velocity in non-vegetated channel can be expressed as:…”

“…where u b is bed load particle velocity in non-vegetated channel, τ * g is non-dimensional value of grain resistance [τ * g = τ g /{(ρ s − ρ)gd 50 }], G s is the specific gravity of the sediment and equals 2.65, C M is the added mass coefficient for sediment particles in water, which has a theoretical value of 0.5 for spherical particles [38], ω 1 and ω 2 are coefficients that correlate bed load saltation length to non-dimensional bed shear stress originated in Equations ( 12) and ( 13) in Shim and Duan [37]. Bed load velocity in vegetated channels is assumed to be proportional to the one in non-vegetated channels as:…”