Inconsistent Spectral Evolution in Operational Wave Models due to Inaccurate Specification of Nonlinear Interactions

Abstract

The introduction of third-generation (3G) models was based on the premise that wave spectra could evolve without prior shape restrictions only if the representation for nonlinear interactions contained as many degrees of freedom as the discretized spectrum being modeled. It is shown here that a different criterion is needed to accurately represent nonlinear spectral evolution within models, a more rigorous criterion such that the number of degrees of freedom in the nonlinear source term must be equal to the intrinsic number of degrees of freedom in the theoretical form of this source term, which is larger than the degrees of freedom in the spectrum. Evolution of spectral shapes produced by the current approximation for nonlinear interactions in 3G models, the discrete interaction approximation (DIA), is compared to the full integral solution for three different time scales: 1) relaxation of the equilibrium range following a perturbation, 2) spectral evolution of the equilibrium range during an interval of constant winds, and 3) the evolution of spectral shape during transition to swell during propagation over long distances. It is shown that the operational nonlinear source term produces significant deviations in the evolution of the wave spectra at all of these scales because of its parametric reduction of the number of degrees of freedom and incorrect energy flux scaling. It is concluded that the DIA does not meet the critical criterion for allowing a spectrum to evolve to spectral shapes consistent with those observed in nature.