Sediment dynamics. Part 1. Bed-load transport by laminar shearing flows
- 25 September 2009
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 636, 295-319
- https://doi.org/10.1017/s0022112009007915
Abstract
We propose a two-phase model having a Newtonian rheology for the fluid phase and friction for the particle phase to describe bed-load transport in the laminar viscous regime. We have applied this continuum model to sediment transport by viscous shearing flows. The equations are shown to reduce to the momentum equation for the mixture and the Brinkman equation for the fluid velocity. This modelling is able to provide a description of the flow of the mobile granular layer. At some distance from threshold of particle motion, where the continuum approach is more realistic as the mobile layer is larger than one particle diameter, there is very little slip between the two phases and the velocities inside the mobile bed have approximately a parabolic profile. When the Poiseuille (or Couette) flow is not significantly perturbed, simple analytical results of the particle flux varying cubically with the Shields number and of the bed-load thickness varying linearly with it can then be obtained. These predictions compare favourably with experimental observations of bed-load transport in pipe flows.Keywords
This publication has 34 references indexed in Scilit:
- Erosion of a granular bed driven by laminar fluid flowJournal of Fluid Mechanics, 2008
- Flow of dense granular material: towards simple constitutive lawsJournal of Statistical Mechanics: Theory and Experiment, 2006
- Ripple formation on a particle bed sheared by a viscous liquid. Part 1. Steady flowJournal of Fluid Mechanics, 2006
- Onset of erosion and avalanche for an inclined granular bed sheared by a continuous laminar flowPhysics of Fluids, 2005
- A general formula for non-cohesive bed load sediment transportEstuarine, Coastal and Shelf Science, 2005
- Erosion and deposition of particles on a bed sheared by a viscous flowJournal of Fluid Mechanics, 2004
- Instability of a bed of particles sheared by a viscous flowJournal of Fluid Mechanics, 2002
- The first effects of fluid inertia on flows in ordered and random arrays of spheresJournal of Fluid Mechanics, 2001
- Moderate-Reynolds-number flows in ordered and random arrays of spheresJournal of Fluid Mechanics, 2001
- The flow of cohesionless grains in fluidsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1956