Scaling laws of plume-induced granular cratering

Extraterrestrial landing often requires firing a high-speed plume towards a planetary surface, and the resulting gas-granular interactions pose potential hazards to the lander. To investigate these jet-induced cratering dynamics, an experiment campaign covering a range of gas and granular properties relevant to the lunar and Martian environments was conducted in a large-scale vacuum chamber. Despite the variations in jet Mach number, mass flow rate, and composition of the granular phase investigated in this work, the observed time evolution of crater depth displays a consistent transition from an early-stage linear to a late-stage sublinear growth. To explain these scaling relations, a model that relates the kinetic energy gained by the particles per unit time to the power of the impinging jet is introduced. From this model, erosion rates and the critical depth at which the transition occurs can be extracted, and they are shown to depend on the gas impingement pressure, which was varied by changing ambient pressure, jet Mach number, mass flow rate, and nozzle height above the surface. These results highlight key mechanisms at work in the dynamics of plume-induced cratering and help to develop an understanding of optimal rocket engine firing times for future landings.