Work-based criterion for particle motion and implication for turbulent bed-load transport

Abstract

A simple work-based criterion for the onset of downstream migration of a particle sitting on a rough bed in a turbulent flow is developed in the present work. The criterion is motivated by the fact that the geometric pocket formed by other bed particles within which the mobile particle is sitting can be viewed as a potential well and the gravitational and frictional mechanisms impose an energy barrier for the particle to fully escape the pocket and initiate irreversible downstream migration. The energy barrier is clearly a statistical quantity, as it depends on the shape, size, and other details of the mobile particle and the geometry of the pocket. The energy barrier imposes a threshold value for the hydrodynamic work that must be done on the particle in order to initiate downstream migration. The simple work-based criterion developed here is related to the critical force and critical impulse criteria that have been advanced in the past. The fluctuating nature of the effective hydrodynamic force that works towards dislodging the particle out of the pocket and migrating it downstream is explored with data from a direct numerical simulation of turbulent channel flow and the probabilities of instances when the force, impulse, and work-based criteria for particle motion are satisfied and computed. The work-based criterion for particle migration is used to obtain an expression for the bed load transport that can be applied on an instantaneous basis at any local region of the bed. The average nondimensional bed load transport rate, or Einstein number, computed based on the present work-based model is shown to compare well with existing experimental data and empirical models. In particular, at low mobility regime, the present model is able to naturally recover the well-accepted rapid increase in bed load transport as 16th power of average bed shear stress and at high mobility regime the present model captures the slower increase in bed load transport with increasing average bed shear stress.

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

“…Lee et al () derived an alternate expression for short turbulent fluctuation events. Instead of a pure rolling motion, they considered entrainment into a combined rolling and sliding motion (however, note that rolling is usually the preferred mode of entrainment) without bed slope ( ), assuming that the associated tangential motion is described by a Coulomb friction law with friction coefficient .…”

“…Furthermore, instead of the pivoting angle, they described the pocket geometry by the horizontal ( ) and vertical ( ) particle displacement (in units of ) that is needed for the particle to escape (equivalent to in Figure ). The expression by Lee et al () reads where is an effective hydrodynamic force and its critical value. For entrainment into a hopping motion, defined as a lift force‐induced particle uplift by a vertical distance , Valyrakis et al () derived …”

“…where F t = F D sin + F L cos and F n = −F D cos + F L sin are the tangential and normal components, respectively, of the driving flow force at the rest position, m p = 1 6 p d 3 is the particle mass, F tc = m p g cos( + )∕ sin − (m p g∕s) cot the resisting force, L arm the lever arm length, C m = 1∕2 the added mass coefficient, and ( , , s) = cos( + ) sin + [1 − sin( + )](cos − 1∕s), with the bed slope angle and the pivoting angle ( Figure 5). For many conditions, this expression can be well approximated by Lee et al (2012) derived an alternate expression for short turbulent fluctuation events. Instead of a pure rolling motion, they considered entrainment into a combined rolling and sliding motion (however, note that rolling is usually the preferred mode of entrainment) without bed slope ( = 0), assuming that the associated tangential motion is described by a Coulomb friction law with friction coefficient C .…”

The Cessation Threshold of Nonsuspended Sediment Transport Across Aeolian and Fluvial Environments

“…Mean flow entrainment models derive a transport initiation threshold Shields number from a force balance, and/or torque balance, between mean fluid forces and resisting contact forces acting on a representative particle resting on the bed surface (Agudo et al, 2017;Ali & Dey, 2016;Bagnold, 1936Bagnold, , 1941Bravo et al, 2014Bravo et al, , 2017Claudin & Andreotti, 2006;Dey, 1999Dey, , 2003Dey & Papanicolaou, 2008;Duan et al, 2013;Durán et al, 2011;Edwards & Namikas, 2015;He & Ohara, 2017;Iversen et al, 1976Iversen et al, , 1987Iversen & White, 1982;Lee et al, 2012;Lehning et al, 2000;Ling, 1995;Lu et al, 2005;Luckner & Zanke, 2007;Recking, 2009;Rousar et al, 2016;Schmidt, 1980;Shao & Lu, 2000;Vollmer & Kleinhans, 2007;Ward, 1969;Wiberg & Smith, 1987;White, 1940;Wu & Chou, 2003). Many of these models have been proposed to reproduce the Shields diagram, which displays two kinds of fluvial thresholds: a threshold obtained from extrapolating measurements of the transport rate to (nearly) vanishing transport and visual measurements of the initiation threshold of individual transport (see section 4.3 for details).…”

A micromechanical modelling approach for predicting particle dislodgement

“…Among different research topics, a major effort has been devoted to the phenomenon of incipient motion of sediment particles. During the past few years, new approaches such as impulse, work, and energy have been proposed to overcome the limitations of the formulation based on the time-averaged Shields parameter and thus improve the prediction of the initiation of sediment particle movement (Diplas et al, 2008;Lee et al, 2012;Valyrakis et al, 2013). The main purpose of these efforts is to relate the fluctuating nature of turbulent flows with the "energy barrier" (Lee et al, 2012) that a particle needs to overcome and thus escape from its resting pocket.…”