Freely decaying weak turbulence for sea surface gravity waves

We study numerically the generation of power laws in the framework of weak turbulence theory for surface gravity waves in deep water. Starting from a random wave field, we let the system evolve numerically according to the nonlinear Euler equations for gravity waves in infinitely deep water. In agreement with the theory of Zakharov and Filonenko, we find the formation of a power spectrum characterized by a power law of the form of |k|−2.5. After the pioneering work by Kolmogorov on the equilibrium range in the spectrum of a homogeneous and isotropic turbulent flow, there have been a number of studies on cascade processes in many other fields of classical physics such as plasma physics, magnetohydrodynamics, and ocean waves. For surface gravity waves, the first seminal theoretical work was performed by O.M. Phillips in 1958, who argued that the frequency spectrum in the inertial range had a specific form. This study expands on those earlier findings, providing a comprehensive analysis of how turbulence manifests in sea surface gravity waves and confirming the theoretical predictions about power spectra in this context.