Abstract Spurious harmonics generation can occur in wave basins when strongly nonlinear waves are generated with linear wave maker theory. For regular long crested waves, the phenomena is known to cause a beating pattern for the amplitude of the higher harmonics, while for irregular waves the effect is often thought to average out. We here report on recent experimental results for spurious harmonic generation for highly nonlinear irregular waves. Long crested waves at two depths are considered. We find a systematic distortion of the spectral shape which is non-uniform in space. The effect occurs in the linear and super harmonic region of the spectrum and is strongest at the smaller depth. We analyze the phenomenon through re-computations in a fully nonlinear wave model and the further application of a four-phase harmonic separation. We next extend the analysis to allow separation of the third- and first-order content of the first-harmonic wave field, by computation at two different amplitudes. The numerical results resembles the measured spectrum closely and the harmonic separation shows that the spectral distortion in the super-harmonic region is to large extent a property of the second-harmonic wave field. Further, the match between the first-harmonic spectrum and the original target spectrum is shown to improve strongly by the removal of the extracted third-order contribution. The observed spectral distortion in the linear frequency region can thus be explained by this third-order field. Returning to the second-order wave field, we demonstrate that the extracted second-order wave field with associated spectral distortion can be reproduced by application of the Sharma and Dean theory with inclusion of the reconstructed spurious wave field from the linear wave generation. Finally, the effect of the spurious second-order harmonic generation on the measured forces is discussed and quantified. We find that the force peak exceedance probability is less influenced by the spurious waves than the spectral shape. We link this to the smaller phase speed of the spurious waves, that makes them arrive later than the main wave packet and thus leads to a limited enhancement of the local peaks.

中文翻译：

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在波槽实验中产生高度非线性的不规则波：杂散谐波及其对波谱的影响

摘要 当利用线性造波器理论产生强非线性波时，波盆中会产生杂散谐波。对于规则的长波峰，已知这种现象会导致高次谐波幅度的跳动模式，而对于不规则的波，这种影响通常被认为是平均的。我们在此报告了针对高度非线性不规则波产生寄生谐波的最新实验结果。考虑了两个深度的长顶波。我们发现光谱形状的系统失真在空间中是不均匀的。该效应发生在频谱的线性和超谐波区域，并且在较小深度处最强。我们通过在完全非线性波模型中重新计算和四相谐波分离的进一步应用来分析该现象。我们接下来扩展分析以允许通过在两个不同幅度下计算来分离一阶谐波波场的三阶和一阶内容。数值结果与实测频谱非常相似，谐波分离表明超谐波区域的频谱畸变在很大程度上是二次谐波场的特性。此外，通过去除提取的三阶贡献，显示出一阶谐波频谱与原始目标频谱之间的匹配性得到显着改善。因此，可以通过该三阶场来解释线性频率区域中观察到的频谱失真。回到二阶波场，我们证明了提取的具有相关频谱失真的二阶波场可以通过应用 Sharma 和 Dean 理论并包含来自线性波生成的重建杂散波场来再现。最后，讨论并量化了伪二次谐波产生对测量力的影响。我们发现力峰值超出概率受杂散波的影响比光谱形状的影响要小。我们将此与杂散波的较小相位速度联系起来，这使得它们比主波包晚到达，从而导致局部峰值的有限增强。讨论并量化了伪二次谐波产生对测量力的影响。我们发现力峰值超出概率受杂散波的影响比光谱形状的影响要小。我们将此与杂散波的较小相位速度联系起来，这使得它们比主波包晚到达，从而导致局部峰值的有限增强。讨论并量化了伪二次谐波产生对测量力的影响。我们发现力峰值超出概率受杂散波的影响比光谱形状的影响要小。我们将此与杂散波的较小相位速度联系起来，这使得它们比主波包晚到达，从而导致局部峰值的有限增强。