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.

Virtual Replica of a Towing Tank Experiment to Determine the Kelvin Half-Angle of a Ship in Restricted Water

“…Alongside these, the critical depth Froude number is depicted to demonstrate the effect of ship speed on the dispersion relation in shallow water. It should be noted that the dispersion relation is speed-independent in deep water [20]. The arms of the loci always begin at , /( / 2 ) = 1 in deep water.…”

“…The spectral method used also performs best at high speeds, where the near-and far-field disturbances generated by the ship are well visible. This can be seen by consulting the results of Caplier et al [20].…”

“…In this section, the method devised by Caplier et al [20] and Gomit et al [22] is briefly examined. This method has previously been used to determine a ship's speed via satellite imagery [46,47].…”

“…A moving ship will cause the waves to be Doppler-shifted, and setting ω = ω − Uk x and k = k, the resulting dispersion relation becomes [20]:…”

“…Therefore, the validation of numerical ship-generated waves is of high importance. In this respect, the work Caplier et al [20], Fourdrinoy et al [21], and Gomit et al [22] is important to mention. The authors of the aforementioned references systematically developed and implemented a technique to capture and analyse ship-generated waves from a model experiment.…”