High-Speed Jet Formation after Solid Object Impact

Abstract

A circular disc hitting a water surface creates an impact crater which after collapse leads to a vigorous jet. Upon impact an axisymmetric air cavity forms and eventually pinches off in a single point halfway down the cavity. Two fast sharp-pointed jets are observed shooting up-and downwards from the closure location, which by then has turned into a stagnation point surrounded by a locally hyperbolic flow pattern. This flow, however, is not the mechanism feeding the jets. Using high-speed imaging and numerical simulations we show that jetting is fed by the local flow around the base of the jet, which is forced by the colliding cavity walls. We show how the well-known theory of a collapsing void (using a line of sinks on the symmetry axis) can be continued beyond pinch-off to obtain a new and quantitative model for jet formation which agrees well with numerical and experimental data. DOI: 10.1103/PhysRevLett.102.034502 PACS numbers: 47.55.NÀ, 47.11.Hj, 47.55.DÀ, 47.55.df The most prominent phenomenon when a solid object hits a water surface is the high-speed jet shooting upwards into the air. The basic sequence of events leading to this jet has been studied since Worthington over a century ago: After impact, the intruder creates an air-filled cavity in the liquid which due to hydrostatic pressure immediately starts to collapse, eventually leading to the pinch-off of a large bubble. Two very thin jets are ejected up-, respectively, downwards from the pinch-off point. This finite-time singularity has been intensively studied in recent time [1][2][3][4][5]. Such singularities have been shown to lead to a hyperbolic flow pattern after collapse and thus to the formation of liquid jets [6][7][8][9].As we show in the present work, however, the radial energy focusing towards the singular pinch-off point alone is not sufficient to explain the extreme thinness of jets observed after the impact of a solid object. Instead, this jet formation is shown to depend crucially on the kinetic energy contained in the entire collapsing wall of the cavity even far above the pinch-off singularity. This is in contrast to jets observed in many other situations where narrow confining cavity walls are not present, e.g., for bubbles bursting on a free surface or near a solid wall [9][10][11], wave focusing [12,13], or jets induced by pressure waves [14]. In addition, surface tension in our case turns out to be irrelevant in contrast to capillary-driven scenarios as suggested for Faraday waves [7,8]. In all these cases jetting seems thus to be accomplished by a mechanism different from the one in this Letter. In the case of drop impact [15,16] or gas injection through a needle [3,17], however, the formation of a cavity and its subsequent inertial collapse can sometimes be observed and the present mechanism might be of relevance.Our experimental setup consists of a circular disc with radius R 0 that is pulled through a water surface with velocity V 0 as described in [4]. The velocity V 0 is kept constant throughout the whole process. Globa...

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