Scaling Laws of Ejecta Streaks in Lunar Landings*

From the crewed Apollo missions of the 1960s to the recent Chang’e uncrewed lunar missions, the interaction between the supersonic exhaust and the lunar surface generates a striking ray system of ejecta particles that travel radially outward at high speeds. While this intriguing pattern has been observed in experiments and simulations, the underlying mechanism remains unclear. These radial ejecta streaks were also observed during an experimental campaign using a Mach 5.3 jet impinging on a granular bed within a large-scale vacuum chamber. Our findings reveal that the radial ejecta streaks are caused by the Gortler instability, which, due to the curvature of the extremely underexpanded jet, induces counter-rotating streamwise vortices within the jet shear layer. These vortices impact the ground and entrain particles in their upwash regions. Experimental measurements from both ground tests and the literature show that the number of streaks strongly depends on the jet diameter at impact and the shear layer thickness, further revealing a power-law scaling with the jet pressure ratio. These insights highlight the pivotal role of fluid dynamics in extraterrestrial landings and provide a foundation for mitigating risks in future planetary missions.