A probabilistic description of the bed load sediment flux

1. Theory

David Jon Furbish, Peter K. Haff, John C. Roseberry, Mark Schmeeckle

Research output: Contribution to journalArticle

89 Citations (Scopus)

Abstract

We provide a probabilistic definition of the bed load sediment flux. In treating particle positions and motions as stochastic quantities, a flux form of the Master equation (a general expression of conservation) reveals that the volumetric flux involves an advective part equal to the product of an average particle velocity and the particle activity (the solid volume of particles in motion per unit streambed area), and a diffusive part involving the gradient of the product of the particle activity and a diffusivity that arises from the second moment of the probability density function of particle displacements. Gradients in the activity, instantaneous or time-averaged, therefore effect a particle flux. Time-averaged descriptions of the flux involve averaged products of the particle activity, the particle velocity and the diffusivity; the significance of these products depends on the scale of averaging. The flux form of the Exner equation looks like a Fokker-Planck equation (an advection-diffusion form of the Master equation). The entrainment form of the Exner equation similarly involves advective and diffusive terms, but because it is based on the joint probability density function of particle hop distances and associated travel times, this form involves a time derivative term that represents a lag effect associated with the exchange of particles between the static and active states. The formulation is consistent with experimental measurements and simulations of particle motions reported in companion papers.

Original languageEnglish (US)
Article numberF03031
JournalJournal of Geophysical Research: Earth Surface
Volume117
Issue number3
DOIs
StatePublished - 2012

Fingerprint

bedload
beds
Sediments
sediments
Fluxes
sediment
Probability density function
Fokker Planck equation
products
probability density functions
probability density function
Advection
diffusivity
Travel time
particle
Conservation
gradients
advection-diffusion equation
Derivatives
particle motion

ASJC Scopus subject areas

  • Earth-Surface Processes
  • Geophysics

Cite this

A probabilistic description of the bed load sediment flux : 1. Theory. / Furbish, David Jon; Haff, Peter K.; Roseberry, John C.; Schmeeckle, Mark.

In: Journal of Geophysical Research: Earth Surface, Vol. 117, No. 3, F03031, 2012.

Research output: Contribution to journalArticle

Furbish, David Jon ; Haff, Peter K. ; Roseberry, John C. ; Schmeeckle, Mark. / A probabilistic description of the bed load sediment flux : 1. Theory. In: Journal of Geophysical Research: Earth Surface. 2012 ; Vol. 117, No. 3.
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