Abstract
Since the introduction of the NewWave theory (Lindgren, 1970), focused wave groups are used in physical and numerical studies to investigate the interaction of marine structures and ships with extreme waves. The propagation of such wave groups is associated with high order nonlinearities that can cause considerable deviations from linear and 2nd order predictions. Consequently, nonlinear numerical models or laboratory tests are needed to accurately describe the evolution of focused wave groups. In the present study, we validate a widely used two-phase Reynolds Averaged Navier-Stokes (RANS) solver realised in OpenFOAM with experimental results for the propagation of steep focused wave groups, using a newly developed methodology based on the separation of harmonics. This approach allows for accurate focusing of wave groups and in-detail examination of the individual evolution of the high order terms, as well as identifying the source of discrepancies between experiments and numerical models. The wave groups comprise long-crested broadbanded Gaussian spectra of increasing steepness propagating in intermediate water depth. The contribution of the nonlinear harmonics to the crest height and overall shape of the wave are also discussed, together with the effect of nonlinear wave interactions on the free-wave spectrum. The rapid growth of 3rd and 4th harmonics near focusing as well as the evolution of the free-wave spectrum, cause departures of up to 29% and 22% from analytic linear and 2nd order predictions. The present results demonstrate that RANS-VoF solvers constitute accurate models to propagate nearly breaking waves.
Highlights
The accurate definition of a design wave for offshore structures, vessels and coastal structures is vital for their survivability, preventing sea accidents with environmental consequences and human losses (Haver, 2000)
The harmonics are retrieved with an inverse Fourier transform (IFT) of
Such differences between the present results and the study of Johannessen and Swan (2003) may be attributed in physical terms to the differences in wave spectra and water depth used in the two studies, and to the employed different methods for the separation of harmonics, with the four-wave decomposition guaranteeing here that 3rd and higher bound waves are excluded from the free-wave spectrum
Summary
The accurate definition of a design wave for offshore structures, vessels and coastal structures is vital for their survivability, preventing sea accidents with environmental consequences and human losses (Haver, 2000). The majority of the studies regarding the evolution of unidirectional wave groups in experimental and numerical wave tanks (NWTs) demonstrated that dispersive focusing of unidirectional wave groups leads to a wave crest at focus, the shape and elevation of which is not predicted by either linear or 2nd order wave theory (Baldock et al, 1996; Gibson and Swan, 2007; Johannessen and Swan, 2001; Johannessen and Swan, 2003; Shemer et al, 2007) This is an effect of high order nonlinearities in large transient waves, namely the bound and resonant nonlinearities (Gibson and Swan, 2007).
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