A description of plume-surface interactions and non-dimensional analysis for crater formation

During entry, descent, and landing, the exhaust plume from a spacecraft interacts with a satellite body or planetary surface. This phenomenon, commonly referred to as plume-surface interactions, can lead to spacecraft aerodynamic disturbances and induced heating, ejection of granular material, landing site obscuration, and crater formation. In this manuscript, a thorough review of theory, existing modeling frameworks, and available experimental data are described for crater formation. A method based on non-dimensional analysis and scaling is proposed, and scaling terms are determined using the Buckingham-Pi approach, including a new non-dimensional rate number describing the excavation of granular material. This approach is applied to experiments of round jet impingement on granular beds from available literature. This provides a framework to estimate crater size and shape for plume surface interactions and can be improved as more data becomes available.