A coupled-mode technique for the transformation of ship-generated waves over variable bathymetry regions

In the present work, a coupled-mode technique is applied to the transformation of ship's waves over variable bathymetry regions, characterised by parallel depth-contours, without any mild-slope assumption. This method can be used, in conjunction with ship's near-field wave data in deep water or in constant-depth, as obtained by the application of modern (linearised or non-linear) ship computational fluid dynamic (CFD) codes, or experimental measurements, to support the study of wave wash generated by fast ships and its effects on the nearshore/coastal environment.

Under the assumption that the ship's track is straight and parallel to the depth-contours, and relatively far from the bottom irregularity, the problem of propagation–refraction–diffraction of ship-generated waves in a coastal environment is efficiently treated in the frequency domain, by applying the consistent coupled-mode model developed by Athanassoulis and Belibassakis J. Fluid Mech. 1999;389] to the calculation of the transfer function enabling the pointwise transformation of ship-wave spectra over the variable bathymetry region.

Numerical results are presented for simplified ship-wave systems, obtained by the superposition of source–sink Havelock singularities simulating the basic features of the ship's wave pattern. The spatial evolution of the ship-wave system is examined over a smooth but steep shoal, resembling coastal environments, both in the subcritical and in the supercritical case. Since any ship free-wave system, either in deep water or in finite depth, can be adequately modelled by wavecut analysis and suitable distribution of Havelock singularities e.g. as presented by Scrags 21st Int. Conf. Offshore Mech. Arctic Eng., OMAE2002, Oslo, Norway, June 2002], the present method, in conjunction with ship CFD codes, supports the prediction of ship wash and its impact on coastal areas, including the effects of steep sloping-bed parts.