PLASMA, HYDRO- AND GAS DYNAMICS

Wind-driven sea spectra resilience as a statistical attractor

A. N. Pushkarev^ab, V. V. Geogjaev^ac, S. I. Badulin<sup>ac

a</sup> Skolkovo Institute of Science and Technology, Moscow, 121205 Russia
^b Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991 Russia
^c Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, 117997 Russia

Abstract: 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 behavior 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.

Received: 14.10.2024
Revised: 01.11.2024
Accepted: 07.11.2024

DOI: 10.31857/S0370274X24120162

 English version: Journal of Experimental and Theoretical Physics Letters, 2024, 120:12, 891–897