Washboard Road: The dynamics of granular ripples formed by rolling wheels

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.