Numerical and analytical calculations of the parameters of power-law spectra for deep water gravity waves

We determine the asymptotic behavior of the coupling coefficient for four-wave interactions of gravity waves in deep water in the limiting case when two wave vectors of interacting waves are small with respect to the other two (“long-short interactions”). It makes possible to find numerically dimensionless Kolmogorov constants for the power-law Kolmogorov–Zakharov spectra. The results obtained are crucially important for comparison of the weak turbulent theory with the experiments and natural observations.