Skimming impact of a thin heavy body on a shallow liquid layer

Abstract

This study addresses the question of whether a thin, relatively heavy solid body with a smooth under-surface can skim on a shallow layer of liquid (for example water), i.e. impact on the layer and rebound from it. The body impacts obliquely onto the liquid layer with the trailing edge of the underbody making the initial contact. The wetted region then spreads along the underbody and eventually either retracts, generating a rebound, or continues to the leading edge of the body and possibly leads to the body sinking. The present inviscid study involves numerical investigations for increased mass ( $M$ , in scaled terms) and moment of inertia ( $I$ , proportional to the mass) together with an asymptotic analysis of the influential parameters and dynamics at different stages of the skimming motion. Comparisons between the asymptotic analysis and numerical results show close agreement as the body mass becomes large. A major finding is that, for a given impact angle of the underbody relative to the liquid surface, only a narrow band of initial conditions is found to allow the heavy-body skim to take place. This band includes reduced impact velocities of the body vertically and rotationally, both decreasing like $M^{-2/3}$ , while the associated total time of the skim from entry to exit is found to increase like $M^{1/3}$ typically. Increased mass thereby enhances the super-elastic behaviour of the skim.