Cylinder water entry on a perturbed water surface

Abstract

The perturbations existing on a breaking wavefront can be a potential explanation for the slamming pressure variability in wave impacts. Here, we investigate the effect of these perturbations by forced vertical slamming of a two-dimensional circular cylinder with constant downward velocity on standing waves. Through experimental modelling and numerical simulation, the slamming force is measured for several standing wave amplitudes and wavelengths. The standing wave phase is tuned such that the impact occurs symmetrically at the instant of maximum crest or trough. Our observations show that slamming coefficients vary with the standing wave amplitude when the wavelength is kept constant and vice versa. The trough impact slamming coefficient can be more than two times the flat impact, and up to four times the crest impact. The experimental results are reproduced by numerical simulations and they agree reasonably well in general. Two analytical approaches based on the von Kármán (NACA, vol. 321, 1929, pp. 1–8) and Wagner (Z. Angew. Math. Mech., vol. 12, 1932, pp. 913–215) methods, which consider the effect of water surface curvature, are introduced. The slamming coefficient calculated from these methods can provide a bound in which the slamming coefficient can be found for each standing wave amplitude and wavelength. Further insight is achieved by numerical simulations of impact on the shorter wavelength to diameter ratio of$0.05<\lambda /D<0.4$. As the wavelength to diameter ratio becomes smaller, the cylinder impacts the water surface at several locations. As a result, multiple peaks occur, and the trapped air at different locations between the cylinder and the water surface yields oscillations with different frequencies on the slamming coefficient time history.