Soliton Turbulence in Approximate and Exact Models for Deep Water Waves

Fluids. 2020. Vol. 5. No. 2. Article 67.

Kachulin D., Dyachenko A., Zakharov V.

We investigate and compare soliton turbulence appearing as a result of modulational
instability of the homogeneous wave train in three nonlinear models for surface gravity waves:
the nonlinear Schrödinger equation, the super compact Zakharov equation, and the fully nonlinear
equations written in conformal variables. We show that even at a low level of energy and average
wave steepness, the wave dynamics in the nonlinear Schrödinger equation fundamentally differ from
the dynamics in more accurate models. We study energy losses of wind waves due to their breaking
for large values of total energy in the super compact Zakharov equation and in the exact equations
and show that in both models, the wave system loses 50% of energy very slowly, during few days.

Keywords: freak waves, nonlinear waves, nonlinear Schrödinger equation, wave breaking, surface gravity waves, super-compact Dyachenko-Zakharov equation, Dyachenko equations