| description abstract | Focused waves are often used in physical and numerical studies as a representative condition for extreme waves or as a means to generate very steep and breaking waves at a prescribed location in space and time. They have also been combined with depth-varying currents in investigations of incipient wave breaking, wave breaking–induced energy dissipation, and wave–current induced loads on marine structures. A focused wave is created when all the components in a transient wave group come into phase. In the past, linear wave theory and iterative methodologies coupled with the linear Doppler-shifted dispersion relationship have been suggested to account for the presence of a current and achieve the required phase and amplitude focusing. In the majority of cases, linear or constant steepness spectra are used, which, compared to measured or theoretical spectra like the Joint North Sea Wave Project (JONSWAP), Gaussian, and Pierson-Moskowitz (PM) can be termed unrealistic. The effectiveness of these methodologies also decreases as the nonlinearity increases; therefore, in most studies, either weakly nonlinear conditions are used or the focus location is determined empirically. Here, an iterative methodology is suggested that can focus waves of any height at a predetermined temporal and spatial location even for wave groups propagating on a strong following or adverse current. An experimental apparatus developed to generate relatively stable sheared velocity profiles is also described. The depth-varying profile of the resulting currents diverges from that of classical wind-driven currents and comes closer to profiles measured in field sites important for the deployment of, for instance, tidal and wind energy converters. The methodology is successfully applied to wave groups traveling on still water, following, and adverse currents, and the results presented refer to linear, weakly nonlinear, and strongly nonlinear–focused waves generated for a range of realistic target spectra. The capability to generate wave groups with the same amplitude spectrum at a fixed location for a variety of flow conditions—still water, following, and adverse sheared currents—is also illustrated. | |
