Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2009-03-26
Phys. Rev. E 79, 061308 (2009)
Nonlinear Sciences
Pattern Formation and Solitons
11 pages, 12 figures, accepted for publication in Phys Rev E
Scientific paper
10.1103/PhysRevE.79.061308
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.
Bitbol Anne-Florence
McElwaine Jim N.
Morris Stephen W.
Taberlet Nicolas
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