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Sensitivity and robustness of Lagrangian coherent structures in coastal water systems

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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.

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Acknowledgements

We thank Professor H. Zhang and Dr. Y. Yu for access to the hydrodynamic model and field data for Moreton Bay. The project is supported through the Australia Research Council Linkage Project grant LP150101172 and Discovery Project grant DP190103379. We thank the two anonymous reviewers for their helpful and constructive comments.

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  1. Environmental Fluid Mechanics Group, Queensland University of Technology (QUT), Brisbane, QLD, 4000, Australia

    Anusmriti Ghosh, K. Suara & Richard J. Brown

  2. School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane, QLD, 4000, Australia

    Scott W. McCue

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  1. Anusmriti Ghosh
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Ghosh, A., Suara, K., McCue, S.W. et al. Sensitivity and robustness of Lagrangian coherent structures in coastal water systems. Environ Fluid Mech 21, 667–691 (2021). https://doi.org/10.1007/s10652-021-09792-8

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