The important basic practical problem of filtering inconsequential short waves that have no significant influence upon the wave drag of a ship that travels at a constant speed in calm water of large depth is considered. This problem is an essential and nontrivial element of the prediction of ship waves within the Neumann-Michell theory, a practical theory useful for routine applications to ship design. A simple analytical relation that explicitly determines the wavenumber of insignificant short waves in terms of the Froude number and three main parameters that characterize the ship hull shape is given. This relation is obtained via a parametric numerical analysis, based on the classical Hogner potential flow model, for a wide range of Froude numbers and thirty hull forms associated with a broad range of nondimensional hull-shape parameters. The relation provides a reliable and particularly simple way of filtering inconsequential short waves that have no appreciable influence upon a ship drag.
The flow around a ship of length L that travels at a constant speed V along a straight path, in calm water of large depth and horizontal extent, is considered within the classical framework of linear potential flow theory, which is realistic and useful for most practical purposes as is well documented; e.g. Noblesse et al (2013a), Huang et al (2013), Yang et al (2013), Ma et al (2017), Ma et al (2018). The Froude number F is defined as
where g denotes the acceleration of gravity.
Within the framework of linear potential flow theory considered here, the flow created by the ship can be formally expressed as the sum of a non-oscillatory local flow component that vanishes rapidly away from the ship and a wave component, dominant in the far field as well as in the nearfield. The local flow component can be evaluated in a straightforward manner, as is shown in Noblesse et al (2011), Wu et al (2016), and is not considered here. The ship waves can be expressed as a linear Fourier superposition of elementary waves, and can also be evaluated very simply via the classical Fourier-Kochin approach; e.g. Noblesse et al (2013a), Huang et al (2013), Zhu et al (2017).