Shock-wave surfing

Abstract

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, is investigated numerically and analytically. During the surfing process, the downstream body can accumulate a significantly higher lateral velocity than would otherwise be possible. The surfing effect is first investigated for interactions between a sphere and a planar oblique shock. Numerical simulations are performed and a simple analytical model is developed to determine the forces acting on the sphere. A phase-plane description is employed to elucidate features of the system dynamics. The analytical model is then generalised to the more complex situation of aerodynamic interactions between two spheres, and, through comparisons with further computations, is shown to adequately predict the final separation velocity of the surfing sphere in initially touching configurations. Both numerical simulations and a theoretical analysis indicate a strong influence of the sphere radius ratio on the separation process and predict a critical radius ratio that delineates entrainment of the smaller body within the flow region bounded by the larger body's shock from expulsion. Furthermore, it is shown that an earlier scaling law does not accurately describe the separation behaviour. The surfing effect has important implications for meteoroid fragmentation: in particular, a large fraction of the variation in the separation velocity 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.