Development of an Equation for Ship Wave Crests in a Current in Whole Water Depths

Abstract

As it increases the construction of large ports and coastal structures, the congestion ratio of large ships is also increasing. Since 1990s, accidents caused by large ship movement have been increasing. And ship waves may cause problems in mooring area. Recently, more marinas are under construction because of increasing of motorboats and yachts. Therefore, ship waves need to be studied to prevent coastal erosion and keep harbor tranquility. When a ship navigates in a channel or an ocean, it creates waves propagating outward in all directions from the source point which is moving with the ship speed. Ship wave crest pattern has been studied since the 1800s. However, there has been no information about the ship wave crest pattern in the whole water depth and high ship speeds. In case of the current existence simultaneously with the navigation of a ship in a river or an ocean, the location of ship wave crests might be different with respect to the direction and the velocity of the current and the ship. Hence, in this study, an equation is developed for the location of crests of ship waves in the current by using the linear dispersion relation for waves in the current. The theoretical solutions of this study are verified with the FLOW-3D’s numerical results for constant water depth. Numerical experiments are conducted by changing ship speeds and current directions while keeping current velocity constant. The developed equations produce close values of cusp locus angles to numerical results. Our results show how far ship wave crests are propagating in the current in the whole water depth and can be also applied in a narrow channel or at a high ship speed.