Saturation of the inverse cascade in surface gravity-wave turbulence*

Wave turbulence models the statistical properties of stochastic nonlinear wave fields. For ocean surface waves, the formation of an inverse cascade towards large scales has been predicted theoretically in the 1980s and confirmed numerically fifteen years ago. By replacing the usual absorbing beach of a wave basin by a reflective wall, we are able to evidence this inverse cascade for the first time in a large-scale basin. We also report a saturation of the evolution of the inverse cascade due to the emergence of nonlinear dissipative structures. In such a statistically stationary and isotropic wave field, we then study the statistics of rogue waves generated by nonlinear wave interactions (and not directly by a wavemaker), a situation thus close to realistic sea states that still remains poorly known.

E. Falcon, G. Michel, G. Prabhudesai, A. Cazaubiel, M. Berhanu, N. Mordant, S. Aumaître, and F. Bonnefoy, Saturation of the inverse cascade in surface gravity-wave turbulence, Phys. Rev. Lett. 125, 134501 (2020).

G. Michel, F. Bonnefoy, G. Ducrozet, and E. Falcon, Statistics of rogue waves in isotropic wave fields, submitted to Phys. Rev. Lett. (2021).