Wind-driven Sea Spectra Resilience as Statistical Attractor

We have observed numerically the resilience phenomenon for ocean wind-driven waves, where the wave spectra return to their original self-similar form after a strong perturbation. This self-similar behaviour is seen as the manifestation of a statistical attractor associated with generalized spectra of Kolmogorov–Zakharov. We have confirmed this interpretation through numerical simulations of random water wave field within the kinetic (Hasselmann) equation. This equation with specific source functions similar to those of conventional wave forecasting models exhibits families of exact self-similar solutions. These source functions minimize the “non-self-similar” background, allowing us to evaluate the “clean rates” of wave spectra resilience. We use the indices of the exact self-similar solutions as parameters for the attractors of numerical solutions in a two-dimensional phase space.