ABSTRACT The present paper aims to incorporate nonlinear amplitude dispersion effects in parabolic and hyperbolic approximation models. First, an explicit and analytical method for considering nonlinearities in parabolic approximation models is investigated. This method follows the concept of calculating spatially and temporally varying wave phase celerities within the simulation. The nonlinear dispersion relation to be applied is dependent on the local Ursell number and wave steepness, in relation to valid regions of analytical wave theories. Furthermore, nonlinearities are introduced in a hyperbolic approximation model by proposing a novel method which combines a parabolic and a hyperbolic model without a significant loss in accuracy, leading to a substantial reduction in the required simulation time. This is achieved by inputting initial boundary conditions into the hyperbolic model based on the output of the parabolic model, which is used for an initial calculation of the spatial distribution of nonlinear dispersion effects over the entire numerical domain. Numerical results were compared with measurements obtained via demanding experimental setups and illustrated satisfactory performance of the models. These concerted nonlinear models offer ease in implementation, short simulation times, and accurate results while incorporating the majority of wave transformation processes including shoaling, refraction, diffraction, reflection, bottom friction and depth-induced wave breaking.

中文翻译：

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用于增强沿海过程模拟的协调非线性缓坡波浪模型

摘要 本文旨在将非线性幅度色散效应纳入抛物线和双曲线近似模型中。首先，研究了在抛物线近似模型中考虑非线性的显式和解析方法。该方法遵循在模拟中计算随空间和时间变化的波相位速度的概念。要应用的非线性色散关系取决于局部 Ursell 数和波陡度，与解析波理论的有效区域有关。此外，通过提出一种结合抛物线和双曲线模型的新方法，在双曲线近似模型中引入了非线性，而不会显着降低精度，从而大大减少所需的仿真时间。这是通过基于抛物线模型的输出将初始边界条件输入双曲线模型来实现的，该模型用于整个数值域上非线性色散效应空间分布的初始计算。将数值结果与通过苛刻的实验设置获得的测量结果进行比较，并说明模型的令人满意的性能。这些协调一致的非线性模型易于实施、模拟时间短、结果准确，同时结合了大部分波浪变换过程，包括浅滩、折射、衍射、反射、底部摩擦和深度引起的波浪破碎。它用于初始计算整个数值域上非线性色散效应的空间分布。将数值结果与通过苛刻的实验设置获得的测量结果进行比较，并说明模型的令人满意的性能。这些协调一致的非线性模型易于实施、模拟时间短、结果准确，同时结合了大部分波浪变换过程，包括浅滩、折射、衍射、反射、底部摩擦和深度引起的波浪破碎。它用于初始计算整个数值域上非线性色散效应的空间分布。将数值结果与通过苛刻的实验设置获得的测量结果进行比较，并说明模型的令人满意的性能。这些协调一致的非线性模型易于实施、模拟时间短、结果准确，同时结合了大部分波浪变换过程，包括浅滩、折射、衍射、反射、底部摩擦和深度引起的波浪破碎。