The natural frequency of the pressure oscillations inside a water-wave entrapped air pocket on a rigid wall

Abstract

Slamming events consisting of an air pocket which is entrapped between a free-surface wave and a rigid structure are considered. This type of impacts occurs during sloshing at a high filling level and as breaking waves impact on sea walls. The air pressure inside this type of air pockets is nearly uniform in space and oscillates in time qualitatively like the free oscillations of a mass–spring system. New analytical natural-frequency formulas are derived for an entrapped air pocket on a vertical wall and for the entrapped air pocket at the upper corner of a sloshing tank. The formulas are verified through comparison with the boundary element method. A comparison between the new analytical formula for entrapped air pockets at the upper corner of a sloshing tank and experiments shows good agreement. The new analytical formula for the entrapped air pocket at a vertical wall is compared with experiments and an existing formula by Topliss et al. (1993). None of the analytical formulas could accurately estimate the natural frequency for this problem. Improved results were obtained by a boundary element method when the geometry of the air pocket and the free surface were fitted accurately. This work shows that the natural frequency is sensitive to both the assumed shape of the air pocket and the shape of the free surface outside the air pocket.