Journal of Engineering Mathematics 48: 353–374, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands. A numerical model for the jet flow generated by water impact D. BATTISTIN and A. IAFRATI INSEAN - Italian Ship Model Basin - via di Vallerano 139 - 00128 Roma, Italy (e-mails: d.battistin@insean.it; a.iafrati@insean.it) Received 2 January 2003; accepted in revised form 14 July 2003 Abstract. In this paper a numerical model is developed aimed at describing the jet flow caused by water impact. The study, carried out in the framework of a potential-flow assumption, exploits the shallowness of the jet region to significantly simplify the local representation of the velocity field. This numerical model is incorporated into a fully nonlinear boundary-element solver that describes the flow generated by the water entry of two-dimensional bodies. Attention is focused on the evaluation of the capability of the model to provide accurate free-surface shape and pressure distribution along the wetted part of the body contour, with particular regard to the jet region. After a careful verification, the proposed model is validated through comparisons with the similarity solution of the wedge impact with constant entry velocity. This similarity solution is derived with the help of an iterative procedure which solves the governing boundary-value problem written in self-similar variables. Key words: jet flow, planing hulls, shallow water, water impact. 1. Introduction Hydrodynamics loads generated during water impact have a rather evident relevance in terms of structural and dynamic response of ships undergoing slamming. The interest in water impact in the naval field is further supported by the relationship between two-dimensional water entry and hydrodynamics of high-speed craft, as it appears by observing the flow field generated by a planing hull in a earth-fixed imaginary plane orthogonal to the advancing velocity. Due to the important implications that water impact has in practice, an intense research activity characterised this field since the pioneering works of von Kármán [1] and Wagner [2]. In particular, much attention has been devoted to obtaining the similarity solution of the problem concerning the water entry, with constant velocity, of two-dimensional wedges. In [3] this solution is obtained in the form of a rather complicated nonlinear, singular, integral equa- tion in terms of the free-surface slope. Later, the same solution has been derived by Hughes [4] with the help of conformal mapping involving Wagner’s function and, very recently, by de Divitiis and de Socio [5] who sought the solution of the problem through a suitable distribution of singularities in a steady potential-flow field. Apart from combined analytical/numerical approaches, accurate and reliable fully nonlinear numerical procedures have been developed aimed at describing the flow field generated during water entry [6]. In spite of the intense research activity, some unresolved issues, requiring deeper invest- igation, still exist. One of these issues concerns the prediction and the modelling of the flow-separation phenomenon that can occur as a result of geometric properties of the body contour. Even for a constant entry velocity, flow can detach from convex contours or from impacting bodies having hard chines. In the latter case separation point can be easily identified