The Kolmogorov spectrum of waves on water is a result of cascading energy via four-wave interactions. For this spectrum in the isotropic case, we introduce basic small perturbations and calculate the decrement of their damping depending on the frequency. We confirm the stability of the Kolmogorov spectrum. The calculation results are applicable for analyzing the stability of numerical methods for solving the kinetic equation. We show that using the discrete-interaction approximation strongly reduces the damping in certain cases.

中文翻译：

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表面重力波 Kolmogorov 谱的稳定性

水上的柯尔莫哥洛夫波谱是通过四波相互作用级联能量的结果。对于各向同性情况下的这个频谱，我们引入了基本的小扰动，并根据频率计算它们的阻尼减量。我们确认了 Kolmogorov 谱的稳定性。计算结果适用于分析求解动力学方程的数值方法的稳定性。我们表明，在某些情况下，使用离散交互近似可以大大降低阻尼。