Abstract When characterising local geometry for unsteady water waves, the accurate determination of spatial quantities such as the wavenumber from measured time traces is non-trivial. The present study investigates different methods in order to highlight the discrepancies that arise when estimating the wavenumber from fully nonlinear numerical time traces of the free surface profile. To this extent, the open research topic relating to the accuracy of the Hilbert transform in analysing broad-banded signals is addressed. The accuracy of local wavenumber estimates from the Hilbert transform are shown to have a strong dependency on the bandwidth of the underlying spectrum. For broad-banded sea-states there is a significant departure of the Hilbert transform predictions from actual wavenumber values. In contrast, the Double Fourier numerical model of Baldock and Swan (1994) [1] is shown to obtain accurate estimates of local wave geometry from just a single measured time trace, regardless of spectral characteristics; it is thus the recommended method. In addition, an empirical correction factor is proposed that can be applied to the linear dispersion equation in order to obtain an improved wavenumber estimate. The correction is tested for unidirectional deep water, nonlinear random sea-states and shown to offer considerable improvements in the local wavenumber estimates.

中文翻译：

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由实测时间轨迹计算波数

摘要 在表征非定常水波的局部几何时，从测量的时间轨迹精确确定波数等空间量是非常重要的。本研究调查了不同的方法，以突出从自由表面轮廓的完全非线性数值时间轨迹估计波数时出现的差异。在这方面，解决了与希尔伯特变换在分析宽带信号中的准确性相关的开放研究课题。来自希尔伯特变换的局部波数估计的准确性被证明对基础频谱的带宽有很强的依赖性。对于宽带海况，希尔伯特变换预测与实际波数值存在显着差异。相比之下，Baldock 和 Swan (1994) [1] 的双傅立叶数值模型表明，无论频谱特征如何，仅从单个测量的时间轨迹即可获得局部波几何的准确估计；因此，这是推荐的方法。此外，还提出了可以应用于线性色散方程的经验校正因子，以获得改进的波数估计。该校正针对单向深水、非线性随机海况进行了测试，并显示出对局部波数估计的显着改进。提出了一个经验校正因子，可以将其应用于线性色散方程以获得改进的波数估计。该校正针对单向深水、非线性随机海况进行了测试，并显示出对局部波数估计的显着改进。提出了一个经验校正因子，可以将其应用于线性色散方程以获得改进的波数估计。该校正针对单向深水、非线性随机海况进行了测试，并显示出对局部波数估计的显着改进。