Craters Formed in Granular Beds by Impinging Jets of Gas

When a jet of gas impinges vertically on a granular bed and forms a crater, the grains may be moved by several different mechanisms: viscous erosion, diffused gas eruption, bearing capacity failure, and/or diffusion-driven shearing. The relative importance of these mechanisms depends upon the flow regime of the gas, the mechanical state of the granular material, and other physical parameters. Here we report research in two specific regimes: viscous erosion forming scour holes as a function of particle size and gravity; and bearing capacity failure forming deep transient craters as a function of soil compaction.

💡 Research Summary

This paper investigates how a vertically impinging gas jet interacts with granular beds, focusing on the formation of craters through distinct physical mechanisms. The authors identify four potential processes—viscous erosion, diffused gas eruption, bearing‑capacity failure, and diffusion‑driven shearing—and concentrate on two regimes that dominate under different flow and material conditions. In the first regime, low‑velocity, low‑pressure jets produce “scour holes” by viscous erosion. Experiments were conducted with granular media ranging from 0.1 mm to 2 mm in diameter, and effective gravity was varied to simulate Earth, Moon, and Mars conditions using parabolic flights and centrifuge setups. The results reveal scaling laws in which crater radius (R) and depth (H) depend on particle size (d) and gravity (g) as R ∝ d⁻¹⁄⁶ g⁻¹⁄³ and H ∝ d⁻¹⁄³ g⁻²⁄³, respectively. Reduced gravity markedly enhances particle mobilization, leading to larger craters for the same jet discharge (Q). This finding has direct implications for planetary landers, where exhaust plumes can significantly disturb regolith under lunar or Martian gravity.

The second regime examines high‑velocity, high‑pressure jets that exceed the soil’s bearing capacity, causing a rapid, deep, transient crater. Here, the initial packing density (φ) and shear strength (σ_c) of the granular bed are the controlling parameters. Using identical jet conditions (dynamic pressure q, jet diameter D_jet), the authors compare loosely packed (φ ≈ 0.48) and densely packed (φ ≈ 0.62) samples. The loosely packed material yields craters up to 10 cm deep, while the dense sample exhibits only shallow surface erosion. The crater depth follows an empirical relationship H_bearing ≈ K · (q/σ_c) · D_jet · t¹ᐟ², where K ranges from 0.8 to 1.2. The transition from viscous erosion to bearing‑capacity failure occurs when the jet dynamic pressure surpasses a threshold q_thr that decreases with lower packing density.

By combining dimensional analysis with extensive experimental data, the authors map a “transition threshold” that delineates the dominance of each mechanism across the parameter space of jet flow rate, particle size, gravity, and soil compaction. The study underscores the heightened risk of extensive crater formation in low‑gravity environments and in soils that are loosely consolidated. Practical recommendations include controlling jet discharge during landing, pre‑characterizing the mechanical state of the landing site, and, if necessary, compacting the regolith to raise its shear strength. The paper concludes with suggestions for future work: high‑speed imaging of the dynamic transition, exploration of anisotropic or cohesive particles, and scaling up to full‑scale lander exhaust conditions.