Abstract

This study investigates the 2D hydrodynamic impact problem of a breaking wave hitting violently a vertical impermeable wall. Our method of solution is analytical. To this end, a slightly overturning breaking wave is simplified in a logical manner. It is assumed that a small air pocket is entrapped between the wall and the wave. The associated mixed boundary value problem (BVP) involves dual trigonometrical series and is solved for the leading order. A perturbation method is applied to cope with the kinematic and dynamic free surface boundary conditions. Results are derived for the velocity potential and the free surface elevation on the wall.

INTRODUCTION

One of the most hazardous cases of hydrodynamic loading on marine structures originate from slamming phenomena (Faltinsen et al., 2004; Faltinsen and Chezhian, 2005; Liang et al., 2016). The dominant feature of this type of loading is the large velocities and accelerations of the fluid particles that violently hit the structure. The hydrodynamic pressures exerted on it, are strongly characterized by their impulsive nature. This means that during impact, a dramatic increase of the pressure in an infinitesimal time interval is observed. Such pressures may lead to high vibrations of some crucial structural elements (whipping). Slamming phenomena could be categorized in water entry problems, breaking wave impacts and green water loading.

Water entry is a widely examined class of impact problems. Since the pioneering works of von Karman (1929) and Wagner (1932), admirable progress has been made. The most in-depth examined body penetrating violently the water surface is the wedge. Dobrovol'skaya (1969) proposed a nonlinear model for the self-similar flow concerning a symmetric wedge with constant entry velocity. Watanabe (1986) obtained a 2D analytical solution for the wedge water entry problem using asymptotic techniques, by calculating inner and outer solutions, and matching them. The study of wedge entry problems has led gradually to the study of more complicated models. A perforated wedge was considered by Molin and Korobkin (2001). Blunt bodies violently penetrating the water free surface, have been examined widely as well (Scolan and Korobkin, 2001). Very recently, Chatjigeorgiou (2019) focused on bodies that form an elliptical contact region. He noted that the solution sought was independent from the angular coordinate.

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