Air-jet impact craters on granular surfaces: a universal scaling

Abstract

Craters form as the lander's exhaust interacts with the planetary surfaces. Understanding this phenomenon is imperative to ensuring safe landings. We investigate the crater morphology, where a turbulent air jet impinges on granular surfaces. To reveal the fundamental aspect of this phenomenon, systematic experiments are performed with various air-jet velocities, nozzle positions and grain properties. The resultant crater morphology is characterized by an aspect ratio. We find a universal scaling law in which the aspect ratio is scaled by a dimensionless variable consisting of the air velocity at the nozzle, the speed of sound in air, the nozzle diameter, the nozzle-tip distance from the surface, the grain diameter, the density of the grains and the density of air. The obtained scaling reveals the cross-over of the length scales governing the crater aspect ratio, providing a useful guideline for ensuring safe landings. Moreover, we report a novel drop-shaped sub-surface cratering phenomenon.