Resonant effects of long-period ship-induced waves near shallow coasts

This work analyzes the propagation properties of long-period ship-induced waves of vessels in confined waterways that are surrounded by wide and shallow water bodies using numerical simulations. Previous measurements indicated that, in the presence of shallow water surroundings, the drawdown being part of the long-period wave system can travel in the form of depression waves over several ship lengths distance [Parnell et al., “Ship-induced solitary Riemann waves of depression in Venice Lagoon,” Phys. Lett. A 379, 555–559 (2015); Scarpa et al., “The effects of ship wakes in the Venice Lagoon and implications for the sustainability of shipping in coastal waters,” Sci. Rep. 9, 19014 (2019)]. The exact conditions leading to these unexpectedly large propagation distances could to date not be clarified [Parnell et al., “Depression Waves Generated by Large Ships in the Venice Lagoon,” J. Coastal Res. 75, 907–911 (2016)]. In this work, evidence from numerical simulations is presented, indicating that the far-field propagation properties are governed by the wave speed of the shallow water surroundings. In case the ship speed is larger than the surrounding wave speed (supercritical conditions), a free wave is continuously generated traveling over the shallow water with only minimal height decay. In the simulations, depression waves can travel over a distance of three ship-lengths with a height reduction below 10% in the supercritical regime, as compared to 80% height reduction in the sub-critical regime. In a one-dimensional environment, this agreement of free and forced wave speed is known as Proudman resonance.