Washboard Road: The Dynamics of Granular Ripples Formed by Rolling Wheels
Physical Review Letters, 99, 068003 (2007).
Nicolas Taberlet , Stephen W. Morris [1, 2] and
Jim N. McElwaine 
 DAMTP, University of Cambridge, Wilberforce Rd, CB3 0WA Cambridge, U.-K.
 Department of Physics,
University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.
Granular surfaces tend to develop lateral ripples under the action
of surface forces exerted by rolling wheels, an effect known as
washboard or corrugated road.
We report the results of both laboratory experiments and soft-particle direct numerical simulations.
Above a critical speed, the ripple pattern appears as small patches of
traveling waves which eventually spread to the entire circumference.
The ripples drift slowly in the driving direction. Interesting
secondary dynamics of the saturated ripples were observed, as well
as various ripple creation and destruction events. All of these
effects are captured qualitatively by 2D soft particle simulations
in which a disk rolls over a bed of poly-disperse particles in a
periodic box. These simulations show that compaction and segregation are inessential to the ripple phenomenon. We also discuss a simplified scaling model which gives some insight into the mechanism of the instability.