Shock-wave surfing and the separation of meteoroid fragments in the atmosphere

Studying the aerodynamic interactions between bodies travelling at highly supersonic speeds is necessary to our understanding of the separation of meteoroid fragments following atmospheric disruption. Here we show that a phenomenon referred to as ``shock-wave surfing,'' in which a body moves in such a way as to follow the shock wave generated by another upstream body, can lead to the accumulation of a significantly higher relative lateral velocity between fragments than would otherwise be possible. The surfing phenomenon is investigated for the canonical cases of interactions between a sphere and a wedge, and between two spheres. Numerical simulations are performed and a simple theoretical model is developed to determine the forces acting on the surfing body. A phase-plane description is employed to elucidate features of the system dynamics in both cases. For the two sphere case, a strong influence of the body radius ratio on the separation process is found and a critical ratio is predicted for initially touching fragments that delineates entrainment of the smaller fragment within the larger fragment's shock from expulsion. It is also shown that a large fraction of the variation in the separation behaviour of meteoroid fragments deduced by previous authors from an analysis of terrestrial crater fields can be explained by a combination of surfing and a modest rotation rate of the parent body.