J. Fluid Mech. (2005), vol. 000, pp. 1–10. c  2005 Cambridge University Press doi:10.1017/S0022112005006373 Printed in the United Kingdom 1 Skipping stones By LIONEL ROSELLINI 1 , FABIEN HERSEN 1 , CHRISTOPHE CLANET 1 , AND LYD ´ ERIC BOCQUET 2 1 IRPHE, UMR 6594, 49 rue F. Joliot-Curie, BP 146, 13384 Marseille, France 2 Laboratoire PMCN, UMR CNRS 5586, Universit´ e Lyon-I, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, France (Received 5 April 2005 and in revised form 22 July 2005) We first report a quantitative experimental study of the collision of a spinning disk with water, from a single to many skips. We then focus on the high spin limit and propose a simple model which enables us to discuss both the physical origin of the bounces and the source of the dissipation which fixes the number of skips. 1. Introduction “One, two, three, four”: this is the number of skips achieved by the stone in figure 1. The rules of competition for skipping stones have never changed (Thomson 2000): a stone or a shell is thrown over a water surface and the maximum number of bounces distinguishes the winner. Part of the attraction of this game comes from the puzzling questions it raises: How can a stone bounce on water? How many skips can it achieve? The impact of objects on water has been the object of a large amount of work in the literature (von K´ arm ´ an 1930; Johnson & Reid 1975; Johnson 1998). Most of these works have focused (mainly due to military applications, e.g. Dambusters) on the impact of spherical and cylindrical objects, and clarified rebound conditions as a function of impact velocity. If R characterizes the size of the object, U its velocity and ρ , ν , σ the fluid properties (respectively density, kinematic viscosity and surface tension) all the above studies are in the limit of large Reynolds number (Re ≡ UR/ν ≫ 1) and large Weber number (ρU 2 R/σ ≫ 1) where inertial effects dominate both viscous and surface forces. Our study belongs to the same domain. However, even if the phenomena at play are similar in the case of stone skipping, the case of a flat (generally spinning) object like a stone is more difficult. In this latter case, a few theoretical analyses have attempted to extract the physical mechanisms (Stong 1968; Crane 1988; Bocquet 2003) and recently, three of us have published the first quantitative experimental results on the first bounce (Clanet, Hersen & Bocquet 2004). This study has motivated extensive numerical simulations (Nagahiro & Hayakawa 2005; Yabe et al. 2005). Here, we first complete our previous results by showing the skipping stone domain in a general phase diagram. Then, we extend the study to several skips and determine the origin of the dissipation responsible for the end of the skipping. 2. Experimental setup The conventions used throughout the article are presented in figure 2: a model stone of thickness h and radius R has a translation velocity U and spinning velocity Ω ≡ Ω n, where n is the unit vector normal to its surface. The orientation of the