Approximate dispersion relations for waves on arbitrary shear flows
Approximate dispersion relations for waves on arbitrary shear flows
复制标题
任意剪切流上波的近似色散关系
DOI：
10.1002/2017jc012994
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Yan Li
中科院分区：
文献类型：
--
作者：
S. Ellingsen;Yan Li
推导并给出了剪切流上的线性表面波的近似色散关系，剪切流的大小和方向随深度任意变化。从势流的一阶偏差推导出的近似，对各种自然发生的剪切流以及广泛使用的模型流在所有波长下都能产生良好的近似。在许多情况下，这种关系可以归结为Skop[1987]常用的近似的三维概化，Kirby和Chen[1989]进一步发展了这种近似，但它被证明更加稳健，在Kirby和Chen模型失败的情况下取得了成功。这两种近似产生相同的数值代价和难度。
An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3D generalization of the much used approximation by Skop [1987], developed further by Kirby & Chen [1989], but is shown to be more robust, succeeding in situations where the Kirby & Chen model fails. The two approximations incur the same numerical cost and difficulty.
While the Kirby & Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability.
A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding 2nd order expression proposed by Kirby \& Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our 2nd order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby & Chen.