Stationary phase and numerical evaluation of far-field and near-field ship waves

A practical method, largely inspired by Kelvin’s stationary-phase approximation, for numerically evaluating the waves created by a ship hull–that advances at constant speed along a straight path in calm water of large depth–is expounded. Unlike alternative numerical methods or the classical stationary-phase analytical approximation that can only be used in restricted regions of the free surface, the method can be applied to compute far-field or near-field waves at arbitrary points of the free surface outside a ship hull. Tests show that a practical number of integration points yield accurate numerical computations in the near field as well as the far field. For validation of the Neumann–Michell theory of ship waves, the method is used to compute the free-surface elevation along longitudinal cuts, for three hull forms at several Froude numbers, and the numerical predictions are compared with experimental measurements.