Abstract

In coastal water systems, horizontal chaotic dispersion plays a significant role in the distribution and fate of pollutants. Lagrangian Coherent Structures (LCSs) provide useful tools to study the problem of the transport of pollutants and have only recently been applied to coastal waters. While the fundamentals of the LCS approach using idealised analytical flow fields are well established in the literature, there are limited studies on their practical implementations in coastal waters where effects of boundaries and bathymetry frequently become significant. Due to their complex bathymetry and boundaries, unstructured grid systems are commonly used in modelling of coastal waters. For convenient derivation of LCS diagnostics, structured grids are commonly used. Here we examine the effect of mesh resolution, interpolation schemes and additive random noise on the LCS diagnostics in relation to coastal waters. Two kinematic model flows, the double gyre and the meandering jet, as well as validated outputs of a hydrodynamic model of Moreton Bay, Australia, on unstructured grids are used. The results show that LCSs are quite robust to the errors from interpolation schemes used in the data conversion from unstructured to structured grid. Attributed to the divergence in the underlying flow field, the results show that random errors in the order of 1–10% cause a breakdown in the continuity of ridges of maximum finite-time Lyapunov exponents and closed orbit elliptic LCSs. The result has significant implications on the suitability of applying LCS formulations based on a deterministic flow field to diffusive coastal waters.

Highlights

• The work examines the sensitivities of applying Lagrangian coherent structure (LCS) diagnostics for coastal waters with complex boundaries.

• LCSs are robust to the errors from interpolation schemes used for unstructured to structured grid velocity data conversion.

• Additive random errors in the order of 1–10 % cause a breakdown in the continuity of ridges of maximum finite-time Lyapunov exponents and closed orbit elliptic LCSs.

中文翻译：

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拉格朗日相干结构在沿海水系统中的敏感性和鲁棒性

摘要

在沿海水系统中，水平混沌扩散在污染物的分布和命运中起着重要作用。拉格朗日相干结构（LCS）提供了有用的工具来研究污染物的运输问题，并且直到最近才应用于沿海水域。尽管使用理想分析流场的LCS方法的基本原理在文献中已得到很好的确立，但对于在边界和水深测量的影响经常变得显着的沿海水域中对它们的实际实现的研究却很少。由于其复杂的测深和边界，非结构化网格系统通常用于沿海水域建模。为了方便派生LCS诊断，通常使用结构化网格。在这里，我们检查网格分辨率的影响，LCS诊断中与沿海水域有关的插值方案和加性随机噪声。使用了两种运动学模型流，即双旋流和曲流射流，以及经过验证的澳大利亚莫顿湾水动力模型在非结构化网格上的输出。结果表明，LCS对于从非结构化网格到结构化网格的数据转换中使用的插值方案所产生的误差具有较强的鲁棒性。由于底层流场的差异，结果表明，大约1–10％的随机误差会导致最大有限时间Lyapunov指数和闭合轨道椭圆LCS的脊的连续性崩溃。该结果对将基于确定性流场的LCS配方应用于扩散性沿海水域的适用性具有重大意义。

强调

• 这项工作研究了对具有复杂边界的沿海水域应用拉格朗日相干结构（LCS）诊断的敏感性。

• LCS对用于非结构化到结构化网格速度数据转换的插值方案的错误具有鲁棒性。

• 1-10％数量级的加性随机误差会导致最大有限时间Lyapunov指数和封闭轨道椭圆LCS的脊的连续性崩溃。