Abstract In this work, numerical simulations of steady-state resonant wave system have been conducted by high-order spectral method (HOS) to study its evolution mechanism in deep water. Convergent high-order series solutions of steady-state resonant waves are first obtained by homotopy analysis method (HAM). Theoretical solutions together with disturbances of different orders of magnitude are then served as the initial solutions in HOS. It is found that as more accurate wave components are generated at the initial stage of the numerical simulation, the time that amplitude of the two largest wave components keeps unchanged increases. Steady-state resonant waves with time-independent spectra can be obtained if sufficient number of wave components are generated at the initial stage. At the end of simulation, additional new wave components that have not been considered at the initial stage appear in the spectra due to four-wave resonant interactions. For steady-state resonant waves with random disturbances, the numerical simulations confirm again the existence of steady-state resonant waves. Besides, energy transfer among different components is more remarkable for steady-state resonant waves with small disturbances before the wave breaking.

中文翻译：

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深水共线有限振幅稳态谐振波的数值模拟

摘要 本文采用高阶谱法(HOS)对稳态谐振波系统进行数值模拟，研究其在深水中的演化机制。首先通过同伦分析法（HAM）获得稳态谐振波的收敛高阶级数解。然后将理论解与不同数量级的干扰一起用作 HOS 中的初始解。发现随着数值模拟初始阶段产生更精确的波分量，两个最大波分量的幅度保持不变的时间增加。如果在初始阶段产生足够数量的波分量，则可以获得具有时间无关谱的稳态谐振波。在模拟结束时，由于四波共振相互作用，在初始阶段未考虑的其他新波分量出现在光谱中。对于具有随机扰动的稳态谐振波，数值模拟再次证实了稳态谐振波的存在。此外，对于破波前扰动较小的稳态谐振波，不同成分之间的能量传递更为显着。