Abstract
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.
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