罗索三参数海底地形的二阶水波特性

IF 0.8
Ulf Ehrenmark
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引用次数: 0

摘要

摘要 罗索(Roseau)在其著作《渐近波理论》(North-Holland,1976 年)中提出了唯一已知的浅滩上线性波传播的精确解。值得注意的是,将近半个世纪过去了,该解的唯一特性似乎已被用于验证更广泛的模型,即远场波高的极限值。这项工作的主要目的是纠正这种情况,提供一个强大的计算环境,在这个环境中,可以随机地在表面和内部对解决方案进行全面评估,速度快,精度高。这种 "基准 "解将有助于采用更严格的方法来验证更通用的替代近似模型。本论文对其中一个模型的部分数值结果进行了检验,并在很大程度上证明了本计算结果的正确性。绝对收敛解积分的计算是通过满足一定差分方程的积分分量的三次样条近似来支持的,这项工作还扩展到了具有悬伸的底部剖面,包括悬伸退化为半无限平板的极端情况。二阶解法的进一步发展揭示了平均欧拉流的细节以及随之而来的斯托克斯漂移,从而可以进行质量输运计算;所有这些都通过一系列轮廓图和箭头图说明了整个深度。计算了驱动二次谐波分量的力场,结果与应用于非相同但略微相似剖面的更一般模态扩展模型中的等效力场非常吻合。这进一步验证了该研究中描述的建模方法和应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Second-order water wave properties over Roseau’s three-parameter bottom topography
Summary In his book Asymptotic Wave Theory (North-Holland 1976), Roseau develops the only known exact solution for linear wave propagation over a shoal. Remarkably, almost half a century later, the only properties of that solution which appear to have been used to validate more wide-ranging models are the limiting values of wave height in the far field. The primary aim of this work is to remedy this situation by providing a robust computational setting where the solution may be fully evaluated randomly both on the surface and the interior, speedily and to a high degree of accuracy. Such ‘benchmark’ solutions will facilitate a much more rigorous approach to validation of more general alternative approximation models. One such has some of its numerical results here examined and subsequently largely vindicated by the present calculations. Computation of the absolutely convergent solution integrals is supported by cubic spline approximation of an integrand component which satisfies a certain difference equation and the work is extended to cover bottom profiles with overhang including the extreme case where the overhang degenerates to a semi-infinite flat plate. The further development of solutions at second-order reveals details of mean Eulerian current and the attendant Stokes drift enabling mass transport computations; all illustrated through the entire depth with a range of contouring and arrows plots. The force field that drives a second harmonic component is calculated and shows excellent agreement with its equivalent in the more general modal expansion model applied to a non-identical but somewhat similar profile. This further validates the modelling approach and application described in that work.
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