A Two-Scale Approximation for Efficient Representation of Nonlinear Energy Transfers in a Wind Wave Spectrum. Part II: Application to Observed Wave Spectra

Abstract

Abstract In Part I of this series, a new method for estimating nonlinear transfer rates in wind waves, based on a two-scale approximation (TSA) to the full Boltzmann integral (FBI) for quadruplet wave–wave interactions, was presented, and this new method was tested for idealized spectral data. Here, the focus is on comparisons of the TSA and the discrete interaction approximation (DIA) with the FBI for observed wave spectra from field measurements. Observed wave spectra are taken from a wave gauge array in Currituck Sound and a directional waverider off the coast near the Field Research Facility at Duck, North Carolina. Results show that the TSA compares much more favorably to the FBI than does the DIA, even for cases in which the parametric component of the formulation does not capture the spectral energy distribution very well. These results remain valid for the TSA estimates when the FBI results are significantly affected by the directional distribution of energy. It is also shown that although nonlinear transfers are substantially weaker in swell portions of the spectrum these interactions contribute significantly to the spectral evolution and net energy balance in long-distance swell propagation.