Dynamics of washboard road formation driven by a harmonic oscillator

Granular surfaces subjected to repeated passage often spontaneously develop a corrugated pattern. In this study, we scrutinized the growth dynamics of surface corrugation in a self-rotating sand bed that is traced by the edge of a vertically oscillating arm. We found that both the rotation velocity and the frequency of the oscillator strongly affect the occurrence rate of corrugation as well as the time evolution in the corrugation pattern, due to the intermittent collision between the oscillator and sand bed. We also discovered that the growth dynamics involves two distinct collective modes that describe the translational motion of the corrugation pattern on the sand bed.