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Erosion of a granular bed driven by laminar fluid flow

Published online by Cambridge University Press:  23 May 2008

ALEXANDER E. LOBKOVSKY ,
ASHISH V. ORPE ,
RYAN MOLLOY ,
ARSHAD KUDROLLI  and
DANIEL H. ROTHMAN
ALEXANDER E. LOBKOVSKY
Affiliation:
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
ASHISH V. ORPE
Affiliation:
Physics Department, Clark University, Worcester, MA 01610, USA
RYAN MOLLOY
Affiliation:
Physics Department, Clark University, Worcester, MA 01610, USA
ARSHAD KUDROLLI
Affiliation:
Physics Department, Clark University, Worcester, MA 01610, USA
DANIEL H. ROTHMAN
Affiliation:
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

Motivated by examples of erosive incision of channels in sand, we investigate the motion of individual grains in a granular bed driven by a laminar fluid to give us new insights into the relationship between hydrodynamic stress and surface granular flow. A closed cell of rectangular cross-section is partially filled with glass beads and a constant fluid flux Q flows through the cell. The refractive indices of the fluid and the glass beads are matched and the cell is illuminated with a laser sheet, allowing us to image individual beads. The bed erodes to a rest height hr which depends on Q. The Shields threshold criterion assumes that the non-dimensional ratio θ of the viscous stress on the bed to the hydrostatic pressure difference across a grain is sufficient to predict the granular flux. Furthermore, the Shields criterion states that the granular flux is non-zero only for θ > θc. We find that the Shields criterion describes the observed relationship hr ∝ Q1/2 when the bed height is offset by approximately half a grain diameter. Introducing this offset in the estimation of θ yields a collapse of the measured Einstein number q* to a power-law function of θ − θc with exponent 1.75 ± 0.25. The dynamics of the bed height relaxation are described well by the power-law relationship between the granular flux and the bed stress.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 605 , 25 June 2008 , pp. 47 - 58
Copyright
Copyright © Cambridge University Press 2008

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