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 numer- ically and theoretically. This process can lead to the downstream body accumulating a significantly higher lateral velocity than would otherwise be possible, and thus is of im- portance in situations such as meteoroid fragmentation, in which the fragment separation behaviour following disruption is determined to a large extent by aerodynamic effects. The surfing effect is first investigated in the context of interactions between a sphere and a planar oblique shock. Numerical simulations are performed and a simple theoretical 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 theoretical 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, in particular, the final separation velocity of the surfing sphere in initially touching configurations. Both numerical simulations and theory indicate a strong influence of the body radius ratio on the separation process and predict a critical radius ratio for initially touching fragments that delineates entrainment of the smaller fragment within the larger fragment’s shock from expulsion; this critical ratio also results in the most extended surfing. Further, these results show that an earlier prediction for the separation velocity to scale with the square root of the radius ratio does not accurately describe the separation behaviour. The theoretical model is then employed to investigate con- figurations with varying initial relative sphere positions and velocities. A phase-space description is also shown to be useful in elucidating the dynamics of the sphere-sphere system. With regard to meteoroid fragmentation, it is shown that a large fraction of the variation in the separation behaviour 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. Finally, a selection effect for multiple fragments travelling together, e.g., immediately following atmospheric disruption, is predicted, whereby larger fragments repel one another whereas smaller fragments are entrained within the shocks of larger bodies.