Abstract The model of coastal waves based on the depth-averaging of the large eddy simulation equations (Kazakova and Richard, 2019) is extended to the case of regular and irregular wave trains. To take into account a stronger turbulence, the third moment of the horizontal velocity is modelled with a gradient-diffusion hypothesis. The effect of this new diffusive term is to smooth and regularize the solutions. An asymptotically equivalent model including the improvement of the dispersive properties is solved with a Discontinuous Galerkin numerical scheme. The model has a low sensitivity to the space discretization parameters. Several classical test cases of wave trains are used to validate the model. In the shoaling zone, the model is similar to the Serre–Green–Naghdi equations but the inclusion of a variable called enstrophy to take into account the large-scale turbulence and the non-uniformity of the mean velocity improves the predictive ability in the inner surf zone. In particular, the turbulent energy of the model is dissipated within one wave cycle and is transported shoreward in the case of waves with a long period whereas, in the case of short periods, it is mostly transported seaward because its dissipation is far from being complete within one period. The case of an irregular wave train propagating over a submerged bar is simulated without any breaking criterion. This benchmark test case validates further the model’s ability in predicting the nonlinear effects due to shoaling, breaking, propagation in a shallow horizontal part and in a deeper region.

中文翻译：

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海岸波列和波浪破碎建模

摘要 基于大涡模拟方程（Kazakova and Richard，2019）深度平均的海岸波模型被扩展到规则和不规则波列的情况。考虑到更强的湍流，水平速度的三次矩用梯度扩散假设建模。这个新的扩散项的作用是平滑和正则化解决方案。使用不连续伽辽金数值方案求解包括色散特性改进的渐近等效模型。该模型对空间离散化参数的敏感性较低。几个经典的波列测试用例用于验证模型。在浅滩区，该模型类似于 Serre-Green-Naghdi 方程，但包含一个称为 enstrophy 的变量以考虑大尺度湍流和平均速度的不均匀性，提高了内海浪区的预测能力。特别是模型的湍流能量在一个波浪周期内耗散，在波浪周期长的情况下向岸边输送，而在短周期的情况下，由于其耗散远未完全，多向海输送。一个时期内。在没有任何破坏准则的情况下，模拟了不规则波列在水下杆上传播的情况。该基准测试案例进一步验证了模型预测由于浅水水平部分和更深区域中的浅滩、破碎、传播引起的非线性效应的能力。