Abstract Waveforms described by the second-order Stokes-type approximations are prone to display anomalous troughs with spurious negative crests. The systemic occurrence of such physically unrealistic features restricts the range of relative validity of second-order models and causes serious errors in modeling the statistics of sea-surface elevations, especially in intermediate and shallow water depths. As a case of practical importance in this regard, this study focuses on and elaborates the nature of the second-order finite-depth narrowband model. A critical review of the conventional formulation of this model reveals that its range of applicability as a statistically viable model of irregular waves is severely limited at relatively shallow water depths. However, a subsequent analysis allows the same model to be modified and reduced to a simpler stochastic form with an attendant first-order probability structure free of anomalies from deep to shallow water depths. Comparisons with laboratory and field data representative of highly nonlinear waves in the shoaling and surf zones indicate that given the skewness coefficient, the modified model provides predictions in general agreement with the distributions of observed surface elevations. It also offers relative simplicity and a wider range of applicability than some other models previously proposed elsewhere.

中文翻译：

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中浅水深海面海拔分布

摘要 由二阶斯托克斯型近似描述的波形容易显示异常波谷和虚假负波峰。这种物理上不切实际的特征的系统性出现限制了二阶模型的相对有效性范围，并导致海面高程统计建模出现严重错误，特别是在中浅水深度。作为在这方面具有实际重要性的一个案例，本研究重点关注并阐述了二阶有限深度窄带模型的性质。对该模型的常规公式的批判性审查表明，它作为不规则波浪的统计上可行的模型的适用范围在相对较浅的水深受到严重限制。然而，随后的分析允许修改相同的模型并将其简化为更简单的随机形式，并附带一阶概率结构，没有从深水到浅水深度的异常。与代表浅滩和冲浪区高度非线性波的实验室和现场数据的比较表明，给定偏度系数，修改后的模型提供的预测与观测到的表面高程分布基本一致。与之前在别处提出的其他一些模型相比，它还提供了相对简单和更广泛的适用性。与代表浅滩和冲浪区高度非线性波的实验室和现场数据的比较表明，给定偏度系数，修改后的模型提供的预测与观测到的表面高程分布基本一致。与之前在别处提出的其他一些模型相比，它还提供了相对简单和更广泛的适用性。与代表浅滩和冲浪区高度非线性波的实验室和现场数据的比较表明，给定偏度系数，修改后的模型提供的预测与观测到的表面高程分布基本一致。与之前在别处提出的其他一些模型相比，它还提供了相对简单和更广泛的适用性。