Abstract A general framework for wave separation in the frequency domain is presented and evaluated with successful results using theoretical examples of nonlinear waves. This framework consists of a qualitative and a quantitative analysis. The qualitative analysis is a novel approach that provides useful information about the existing wave trains within a wave field. This information includes an estimation of the number of wave trains, their direction of propagation (seaward or shoreward), their nature (free or bound) and their relative importance. The quantitative analysis consists in a revisited wave separation method applicable to separate free and bound wave trains travelling seaward and shoreward for both high and low frequencies propagating over uneven bathymetries. This versatility represents an improvement compared to existing methods. The presented separation method is low-sensitive to noise and its robustness is tested for a range of wave separation settings. The potential application of the separation method to random waves is discussed.

中文翻译：

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频域中波分离的通用框架

摘要 提出了频域中波分离的一般框架，并使用非线性波的理论实例对成功结果进行了评估。该框架由定性分析和定量分析组成。定性分析是一种新颖的方法，可提供有关波场内现有波列的有用信息。该信息包括对波列数量的估计、它们的传播方向（向海或向岸）、它们的性质（自由或约束）及其相对重要性。定量分析包括重新审视的波浪分离方法，该方法适用于分离向海和向岸行进的自由和束缚波列，用于在不均匀的水深上传播的高频和低频。与现有方法相比，这种多功能性代表了一种改进。所提出的分离方法对噪声的敏感性较低，并且针对一系列波分离设置测试了其稳健性。讨论了分离方法对随机波的潜在应用。