The dispersive characteristics of unidirectional irregular waves propagating and breaking over a mildly sloping beach are examined using a highly-resolved laboratory dataset. Cross-spectral analyses are used to determine the cross-shore evolution of (single-valued) dominant wavenumber κ and phase velocity c spectra, and lead to the identification of four different regimes of propagation: I - a linear regime where short waves mostly propagate as free components; II - a shoaling regime where non-linear effects at high harmonics are significant but primary components follow the linear wave dispersion relation; III - a shoaling regime near the mean breaking point location, where amplitude dispersion effects at primary components are important; IV - a surf zone regime, where all components propagate slightly faster than non-dispersive shallow water waves. Bispectral analyses performed onshore of the shoaling region show that the presence of forced energy at high harmonics, which originate from non-linear interactions between triads of frequencies, are responsible for the deviations of wavenumber and phase velocity spectral estimates from predictions by the linear dispersion relation, confirming the findings from previous field-based studies. A Boussinesq approximation of the non-linear energy exchanges between triads is then used to quantify the relative amount of forced energy at high harmonics and explain the differences in dispersion properties observed in the shoaling region between broad and narrow-band spectra. Larger relative amounts of forced energy at high frequencies, which suggest more efficient non-linear energy transfers, are found to be associated with larger deviations of dominant κ and c from predictions by the linear dispersion relation.

使用高度解析的实验室数据集检查了在缓坡海滩上传播和破裂的单向不规则波的色散特性。跨谱分析用于确定（单值）主波数κ和相速度c的跨岸演化光谱，并导致识别出四种不同的传播方式：I-一种线性方式，其中短波主要以自由成分的形式传播；II-一种浅滩制度，其中高次谐波的非线性影响显着，但主要成分遵循线性波频散关系；III-在平均断点位置附近的浅滩制度，在该制度中，主要分量处的振幅色散效应很重要；IV-冲浪区制度，其中所有成分的传播都比非分散浅水波传播的速度略快。在浅滩区岸上进行的双谱分析表明，高谐波中存在强制能量，这是由三重频率之间的非线性相互作用引起的，通过线性弥散关系，波数和相速度谱估计值与预测值之间存在偏差，这证实了先前基于野外研究的发现。然后，使用三重轴之间的非线性能量交换的Boussinesq逼近来量化高次谐波下的强制能量的相对量，并解释在宽带频谱和窄带频谱之间的浅滩区域中观察到的色散特性差异。发现在高频下较大的相对强制能量，这表明更有效的非线性能量转移，与较大的主偏差有关。然后，使用三重轴之间的非线性能量交换的Boussinesq逼近来量化高次谐波下的强制能量的相对量，并解释在宽带频谱和窄带频谱之间的浅滩区域中观察到的色散特性差异。发现在高频下较大的相对强制能量，这表明更有效的非线性能量转移，与较大的主偏差有关。然后，使用三重轴之间的非线性能量交换的Boussinesq逼近来量化高次谐波下的强制能量的相对量，并解释在宽带频谱和窄带频谱之间的浅滩区域中观察到的色散特性差异。发现在高频下较大的相对强制能量，这表明更有效的非线性能量转移，与较大的主偏差有关。根据线性色散关系从预测得出κ和c。