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Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains. (English) Zbl 1441.65122

Summary: We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: black-hole vortices [G. Haller and F. J. Beron-Vera, J. Fluid Mech. 731, R4, 10 p. (2013; Zbl 1294.76188)], objective Eulerian Coherent Structures (OECSs) [M. Serra and G. Haller, Chaos 26, No. 5, 053110, 17 p. (2016; Zbl 1361.37020)], material barriers to diffusive transport [G. Haller et al., Proc. Natl. Acad. Sci. USA 115, No. 37, 9074–9079 (2018; Zbl 1416.76303); G. Haller et al., SIAM J. Appl. Dyn. Syst. 19, No. 1, 85–123 (2020; Zbl 1448.76146)], and constrained diffusion barriers [G. Haller et al., SIAM J. Appl. Dyn. Syst. 19, No. 1, 85–123 (2020; Zbl 1448.76146)]. The method builds on ideas developed previously in [D. Karrasch et al., Proc. A, R. Soc. Lond. 471, No. 2173, Article ID 20140639, 13 p. (2015; Zbl 1371.76044)], but our implementation alleviates a number of shortcomings and allows for the fully automated detection of such vortices on unprecedentedly challenging real-world flow problems, for which specific human interference is absolutely infeasible. Challenges include very large domains and/or parameter spaces. We demonstrate the efficacy of our method in dealing with such challenges on two test cases: first, a parameter study of a turbulent flow, and second, computing material barriers to diffusive transport in the global ocean.

MSC:

65P10 Numerical methods for Hamiltonian systems including symplectic integrators
76F70 Control of turbulent flows
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References:

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