Wave forecasting in ocean and coastal waters commonly relies on spectral models based on the spectral action balance equation. These models assume that different wave components are statistically independent and as a consequence cannot resolve wave interference due to statistical correlation between crossing waves, as may be found in, for instance, a focal zone. This study proposes a statistical model for the evolution of wave fields over non-uniform currents and bathymetry that retains the information on the correlation between different wave components. To this end, the quasi-coherent model (Smit & Janssen, J. Phys. Oceanogr. , vol. 43, 2013, pp. 1741–1758) is extended to allow for wave–current interactions. The outcome is a generalized action balance model that predicts the evolution of the wave statistics over variable media, while preserving the effect of wave interferences. Two classical examples of wave–current interaction are considered to demonstrate the statistical contribution of wave interferences: (1) swell field propagation over a jet-like current and (2) the interaction of swell waves with a vortex ring. In both examples cross-correlation terms lead to development of prominent interference structures, which significantly change the wave statistics. Comparison with results of the SWAN model demonstrates that retention of cross-correlation terms is essential for accurate prediction of wave statistics in shear-current-induced focal zones.

中文翻译：

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对剪切流上的统计波干扰建模

海洋和沿海水域的波浪预测通常依赖于基于光谱作用平衡方程的光谱模型。这些模型假设不同的波分量在统计上是独立的，因此无法解决由于交叉波之间的统计相关性而导致的波干扰，例如可能在聚焦区中发现的。这项研究提出了一个统计模型，用于在非均匀海流和水深测量上的波场演化，该模型保留了不同波分量之间相关性的信息。为此，准相干模型 (Smit & Janssen, J. Phys. Oceanogr., vol. 43, 2013, pp. 1741–1758) 被扩展到允许波-流相互作用。结果是一个广义的动作平衡模型，可以预测波动统计在可变介质上的演变，同时保留波干扰的影响。波-流相互作用的两个经典例子被认为可以证明波干扰的统计贡献：（1）涌流场在喷射状流上的传播和（2）涌流与涡环的相互作用。在这两个例子中，互相关项导致显着干扰结构的发展，这显着改变了波统计。与 SWAN 模型的结果进行比较表明，保留互相关项对于准确预测剪切电流诱导的焦点区域中的波浪统计数据至关重要。(1) 涌流场在喷射状电流上的传播和 (2) 涌流波与涡环的相互作用。在这两个例子中，互相关项导致显着干扰结构的发展，这显着改变了波统计。与 SWAN 模型的结果进行比较表明，保留互相关项对于准确预测剪切电流诱导的焦点区域中的波浪统计数据至关重要。(1) 涌流场在喷射状电流上的传播和 (2) 涌流波与涡环的相互作用。在这两个例子中，互相关项导致显着干扰结构的发展，这显着改变了波统计。与 SWAN 模型的结果进行比较表明，保留互相关项对于准确预测剪切电流诱导的焦点区域中的波浪统计数据至关重要。