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.