Energy distribution in shallow water ship wakes from a spectral analysis of the wave field

Abstract

This work presents an experimental study of the effects of finite water depth on the waves generated by a ship in a towing tank. The wakes of two hull forms representative of maritime and river ships are measured for both deep water and shallow water configurations and for several Froude numbers. The free surface deformations are measured with an optical stereo-correlation measurement method to access a full and detailed reconstruction of the wave fields. The spatial resolution of the reconstructed wakes allows us to perform a spectral analysis of the waves generated by the ships and to decompose them into a near-field hydrodynamic response and a far-field undulatory component. First, the spectral analysis method is presented and the effects of finite water depth on a theoretical point of view are studied. The analysis of subcritical, trans-critical, and supercritical ship wakes in both real space and spectral space highlights the effects of the finite water depth, of the ship speed, and of the hull shape on the energy distribution in the ship wakes through these different regimes.