Scaling and dynamics of washboard road Physical Review E, 79, 061308 (2009). Anne-Florence Bitbol [1,2], Nicolas Taberlet [1], Stephen W. Morris [3] and Jim N. McElwaine [2] [1] Universite de Lyon, Ecole Normale Superieure de Lyon, Laboratoire de Physique, 46 allee d'Italie, 69007 Lyon, France [2] DAMTP, University of Cambridge, Wilberforce Rd, CB3 0WA Cambridge, U.-K. [3] Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.

Granular surfaces subjected to forces due to rolling wheels develop ripples above a critical speed. The resulting pattern, known as washboard or corrugated road, is common on dry, unpaved roads. We investigated this phenomenon theoretically and experimentally, using laboratory-scale apparatus and beds of dry sand. A thick layer of sand on a circular track was forced by a rolling wheel on an arm whose weight and moment of inertia could be varied. We compared the ripples made by the rolling wheel to those made using a simple inclined plow blade. We investigated the dependence of the critical speed on various parameters, and describe a scaling argument which leads to a dimensionless ratio, analogous to the hydrodynamic Froude number, which controls the instability. This represents the crossover between conservative, dynamic forces and dissipative, static forces. Above onset, wheel-driven ripples move in the direction of motion of the wheel, but plow-driven ripples move in the reverse direction for a narrow range of Froude numbers.

Movies:

• Video: [YouTube], [Flickr] of the plow in stroboscopic view.
• Video: A long view of the washboard road experiment at DAMTP [YouTube].
• Video: The onset and development of the ripples in slow motion [YouTube].

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