Cratering by the oblique impact of a spinning projectile

Abstract

We investigate the roles of spin and packing fraction on the dynamics of cratering when a solid projectile impacts a granular bed at different incident angles. For that, we carried out DEM (discrete element method) computations in which we varied the magnitude and direction of the projectile spin, the impact velocity, the bed packing fraction, and the incident angle. For a given incident velocity, we found that the projectile can rebound for small angles, or be completely or partially buried for larger angles, and that when buried it can sometimes migrate large horizontal distances depending on the incident angle. We also found that increasing the packing fraction strengthens rebounds, and that the initial spin, depending on its direction and orientation, induces rebound, burying, or transverse deviations. The crater morphology also changes with the varying parameters, acquiring circular, elliptical, goutte-like, tadpole-like, and transitional shapes, correlating well with the projectile behavior. Finally, we propose diagrams organizing and classifying the dynamics observed. Our results shed new light on the different shapes of craters found in nature and the fate of the impacting material.

Figures (12)

• Figure 1: (a) Butterfly crater in the region of Hesperia Planum, on Mars; (b) a recent 20-km-diameter bowl crater on Vesta; (c) elongated crater (78 km in length) in the south of the Huygens crater, on Mars; (d) Orcus Patera crater on Mars (with many circular craters in and around it). Image in panel (b): Courtesy NASA/JPL-Caltech. Images in panels (a), (c) and (d): Courtesy ESA/DLR/FU Berlin (G. Neukum).
• Figure 2: (a) Layout of the numerical setup (the $y$ coordinate points downwards, and, although shown on the bottom, the origin of the coordinate system is on the bed surface centered horizontally in the domain). (b) Numerical result showing the topography (elevation) of a crater formed by an oblique impact. In this figure, $\phi$$=$ 0.559, $\alpha$$=$ 5$^\circ$, $V_p$$=$ 6.5 m/s, and the colorbar shows the elevation from the undisturbed surface (pointing downwards). The longitudinal $L_x$ and transverse $L_z$ dimensions of the crater are shown in the figure.
• Figure 3: Top view of final positions of grains, showing the different shapes of craters found by varying the controlled parameters. (a) Circle, obtained in this figure for $\alpha$$=$ 75$^\circ$, $V_p$$=$ 4 m/s, and $\phi$$=$ 0.559; (b) ellipse, obtained in this figure for $\alpha$$=$ 30$^\circ$, $V_p$$=$ 9 m/s, and $\phi$$=$ 559; (c) tadpole-like crater, obtained in this figure for $\alpha$$=$ 15$^\circ$, $V_p$$=$ 7 m/s, and $\phi$$=$ 0.559; (d) goutte-like crater, obtained in this figure for $\alpha$$=$ 60$^\circ$, $V_p$$=$ 5 m/s, and $\phi$$=$ 0.638. (e) transitional shape, obtained in this figure for $\alpha$$=$ 30$^\circ$, $V_p$$=$ 4 m/s, and $\phi$$=$ 0.590. In all panels, $|\vec{\omega}|$$=$ 0 rad/s. The colorbar on the bottom of each panel shows the elevation of each grain from the undisturbed surface (coordinate pointing downwards), in meters.
• Figure 4: Different fates of the projectile observed in the DEM computations: (a) partial burying, obtained in this figure for $\alpha$$=$ 60$^\circ$, $V_p$$=$ 0.5 m/s, and $\phi$$=$ 0.559; (b) penetration, obtained in this figure for $\alpha$$=$ 60$^\circ$, $V_p$$=$ 4 m/s, and $\phi$$=$ 0.559; (c) subsurface glide, obtained in this figure for $\alpha$$=$ 30$^\circ$, $V_p$$=$ 9 m/s, and $\phi$$=$ 0.559; (d) subsurface rise, obtained in this figure for $\alpha$$=$ 15$^\circ$, $V_p$$=$ 1.5 m/s, and $\phi$$=$ 0.559; (e) retained ricochet, obtained in this figure for $\alpha$$=$ 15$^\circ$, $V_p$$=$ 3 m/s, and $\phi$$=$ 0.559; (f) ricochet, obtained in this figure for $\alpha$$=$ 15$^\circ$, $V_p$$=$ 8 m/s, and $\phi$$=$ 0.559. In all panels, $|\vec{\omega}|$$=$ 0 rad/s. The impact point is shown as an empty circle, the final position as a solid circle, and the trajectory as a solid line.
• Figure 5: Classification maps of crater shapes for non-spinning projectiles. (a)-(c) Maps in the $\alpha$ - Fr space for different packing fractions: $\phi$$=$ 0.559, 0.590 and 0.638, respectively. (d)-(f) Maps in the $\phi$ - Fr space for different impacting angles: $\alpha$$=$ 15$^{\circ}$, 30$^{\circ}$ and 60$^{\circ}$, respectively. The symbols are listed in the key, and the colors (listed also in the key) correspond to the projectile fates presented in Subsection \ref{['fate']}.