This work presents the results of direct numerical simulation of gravity water wave turbulence within a fully nonlinear plane-symmetric model. We show that in 1D geometry, the spectrum of weak turbulence of plane gravity waves generated by five-wave resonant interactions (suggested in [1]) is not realized. Instead of that, the main contribution to turbulence is due to wave breaking, which produces a power-law spectrum in both the frequency range and the wavenumber space with the same exponent equal to −4, see Fig.1. To our knowledge, our results represent the first direct numerical confirmation of the strong turbulence spectra predicted in [2]. In strongly nonlinear regime, the calculated probability density function (PDF) for the surface gradient has power-law tails with exponents close to −7/2, which indicates intermittency in turbulence.

Fig.1. The calculated frequency and spatial spectra of surface perturbations compared to the power-law dependencies ω^-4 and k^-4.

1. A.I. Dyachenko, Y.V. Lvov, V.E. Zakharov, Physica D 87(1-4), 233(1995)

2. E.A.Kuznetsov, JETP Lett. 80(2) ,83 (2004)

E.  Kochurin and E. Kuznetsov
JETP Letters 122, issue 4 (2025)