Washboard Road: The Dynamics of Granular Ripples Formed by Rolling Wheels

We report laboratory experiments on rippled granular surfaces formed under rolling wheels. Ripples appear above a critical speed and drift slowly in the driving direction. Ripples coarsen as they saturate and exhibit ripple creation and destruction events. All of these effects are captured qualitatively by 2D soft-particle simulations in which a disk rolls over smaller disks in a periodic box. The simulations show that compaction and segregation are inessential to the ripple phenomenon. We describe a simplified scaling model which gives some insight into the mechanism of the instability.

Figure 1

Experimental setup. A bed of natural sand is laid on the circumference of a rotating table (1 m in diam and rotation rate between 0.2 and 0.8 Hz). A hard rubber wheel attached to an arm is free to bounce and roll on the granular bed.

Figure 2

Bed profile and wheel trajectory for typical washboard patterns obtained experimentally (a) and numerically (b).

Figure 3

An experimental space-time plot of the vertical position of the wheel for $v=2{\mathrm{ms}}^{-1}$.

Figure 4

Experimental ripple dynamics from Fig. 3. (a) Time evolution of the number of ripples (diamonds) and of the amplitude of the ripples (solid line). (b) Drift velocity in millimeters per rotation, as a function of the number of ripples.

Figure 5

The internal structure of the ripples, using DEM simulation. (a) Grain size, (b) local packing fraction, (c) displacement between two consecutive passes of the wheel.