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Identifying Higher-Order Interactions in Wave Time-Series

机译：识别波时间序列中的高阶交互

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Reliable design and reanalysis of coastal and offshore structures require, among other things, characterization of extreme crest elevation corresponding to long return periods. Extreme crests typically correspond to focused wave events enhanced by wave-wave interactions of different orders - third-order, four-wave interactions dominating in deep water (Janssen, P. A. E. M., 2003, "Nonlinear Four-Wave Interactions and Freak Waves," J. Phys. Oceanogr., 33(4), pp. 863-884). Higher-order spectral (HOS) analysis can be used to identify wave-wave interactions in time-series of water surface elevation; trispectral analysis is needed to detect third-order, four-wave interactions. Four-wave interactions between Fourier components can involve interactions of the type where f 1 + f2 + f3 = f4 and where f 1 + f2 = f3 + f4, resulting in two definitions of the trispectrum - the T- and V-trispectrum (with corresponding tricoherences), respectively. It is shown that the T-tricoherence is capable of detecting phase-locked four-wave interactions of the type f4 = f 1 + f2 + f3 when these are simulated with simple sinusoids, but such interactions were not detected in HOS model simulations and field data. It is also found that high V-tricoherence levels are detected at frequencies at which four-wave interactions of the type f 1 + f2 = f3 + f4 are expected, but these may simply indicate combinations of independent pairs of Fourier components that happen to satisfy the frequency relationship. Preliminary analysis shows that using a cumulant-based trispectrum (Kravtchenko-Berejnoi, V., Lefeuvre, F., Krasnosel'skikh, V. V., and Lagoutte, D., 1995, "On the Use of Tricoherent Analysis to Detect Nonlinear Wave-Wave Interactions," Signal Process., 42(3), pp. 291-309) may improve identification of wave-wave interactions. These results highlight that caution needs to be exercised in interpreting trispectra in terms of specific four-wave interactions occurring in sea states and further research is needed to establish whether this is in fact possible in practice.
机译：沿海和海上结构的可靠设计和再分析需要，除其他外，还需要对应于长返回时期的极端嵴高度的表征。极端波峰通常对应于不同订单的波浪相互作用增强的聚焦波事件 - 三阶，四波相互作用，在深水中（janssen，Paem，2003，“非线性四波相互作用和Freak Waves，”J.物理。Oceanogr。，33（4），pp。863-884）。高阶光谱（HOS）分析可用于识别水面升高时间序列中的波浪相互作用;需要三级分析来检测三阶四波相互作用。傅立叶组件之间的四波相互作用可以涉及类型F 1 + F2 + F3 = F4和其中F 1 + F2 = F3 + F4的类型的相互作用，从而导致T-和V-TRISPECTRUM的两个定义 - T-和V-TRISPECTRUM（相应的三张学）分别。结果表明，当用简单的正弦曲线模拟这些时，T三相起能够检测F4 = F 1 + F2 + F3的锁相锁定的四波相互作用，但在HOS模型模拟和场中未检测到这种相互作用数据。还发现，在预期F 1 + F2 = F3 + F4的四波相互作用的频率下检测高V示波水平，但这些可以简单地指示恰好满足的独立成对的傅里叶组件的组合频率关系。初步分析表明，使用基于累积的Trispectrum（Kravtchenko-berejnoi，V.，Lefeuvre，F.，Krasnosel'skikh，VV和Lagoutte，D.，1995，“，关于使用特写分析来检测非线性波浪波相互作用，“信号过程”，42（3），PP。291-309）可以改善波浪相互作用的识别。这些结果强调，在海域发生的特定四波相互作用方面，需要在解释三角区时进行小心，并且需要进一步研究，以便在实践中确定这是否实际上是可能的。

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