Evaluation of ship waves at the free surface and removal of short waves

The dual basic tasks of evaluating ship waves at the free surface and of removing unwanted short waves are considered within the framework of the ‘free-surface Green function potential flow theory’, based on a Green function that satisfies the radiation condition and the Kelvin–Michell linearized boundary condition at the free surface. A practical approach based on parabolic extrapolation within an extrapolation layer bordering the free surface is used. The height of the extrapolation layer is defined explicitly via simple analytical relations in terms of the Froude number and the slenderness of the ship hull, and varies from the bow to the stern. The bow-to-stern variation is an important ingredient that accounts for the fact that waves along the ship hull aft of the bow wave differ from the bow wave. Indeed, a ship bow wave is significantly higher and shorter than waves aft of the bow wave, is affected by nearfield effects related to the rapid variation of the hull geometry at a ship bow, and consequently contains more short wave components. Illustrative calculations demonstrate the need for removing short ship waves and the effectiveness of the approach based on parabolic extrapolation.