Abstract This paper presents numerical simulations of the propagation, shoaling and run-up of full-scale tsunami waves. The simulations are performed with a model solving Reynolds-averaged Navier-Stokes equations with k-ω turbulence closure, and is one of very few studies involving CFD simulations at full tsunami scale, involving full resolution of small scale dispersive effects as well as wave breaking. It is demonstrated that a combination of previous analytical and empirical expressions for run-up heights and inundation speeds match those simulated well. This indicates that these are reasonable first approximation even in cases where the underlying assumption of linearity of the incoming tsunami is violated, as well as in cases where breaking occurs, though they generally slightly underestimate both run-up height and inundation speed. It is shown that the run-up of tsunamis can manifest in different ways depending on the initial wave shape and slope of the coast, and three qualitative run-up types previously identified in the literature are described in detail. It is further shown that the shorter waves of an undular bore, which appear during lengthy propagation in shallow water, can either maintain their shape the entire distance to shore, or break far offshore creating a breaking bore. It is demonstrated the front of the breaking bore will not appear as steep for N-waves as single waves because these need to re-wet the drawn-down region before reaching the original shoreline. Finally, the importance of shorter waves riding on the front of the tsunami is discussed. It is shown that they have little impact on the run-up height and inundation speed, but are important in terms of local flow velocities. The results presented here are Part 1 of a larger study, where Part 2 involves details of the tsunami-induced boundary layer dynamics, bed shear stresses and implication for sediment transport.

中文翻译：

---

海啸的全尺寸 CFD 模拟。第 1 部分：模型验证和试运行

摘要 本文介绍了全尺度海啸波的传播、浅滩和上升的数值模拟。模拟是通过使用 k-ω 湍流闭合求解雷诺平均 Navier-Stokes 方程的模型进行的，并且是极少数涉及全海啸尺度 CFD 模拟的研究之一，涉及小尺度色散效应的全分辨率以及波浪破碎. 结果表明，先前的分析和经验表达式的组合可以很好地匹配模拟的上升高度和淹没速度。这表明，即使在违反传入海啸线性基本假设的情况下，以及在发生断裂的情况下，这些也是合理的一阶近似值，尽管它们通常略微低估了上升高度和淹没速度。结果表明，海啸的上升可以根据海岸的初始波浪形状和坡度以不同的方式表现出来，并且详细描述了先前在文献中确定的三种定性的上升类型。进一步表明，在浅水中长时间传播期间出现的波状孔的较短波可以在到海岸的整个距离内保持其形状，或者在离岸很远的地方破裂形成破裂孔。事实证明，对于 N 波来说，破裂孔的前部不会像单波那样陡峭，因为它们需要在到达原始海岸线之前重新润湿下降区域。最后，讨论了在海啸前部形成较短波浪的重要性。结果表明，它们对助跑高度和淹没速度的影响很小，但在局部流速方面很重要。此处提供的结果是一项更大研究的第 1 部分，其中第 2 部分涉及海啸引起的边界层动力学、床剪切应力和沉积物迁移的含义的详细信息。