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Distinguished material surfaces and coherent structures in three-dimensional fluid flows. (English) Zbl 1015.76077
Summary: We prove analytic criteria for the existence of finite-time attracting and repelling material surfaces and lines in three-dimensional unsteady flows. The longest living such structures define coherent structures in Lagrangian sense. Our existence criteria involve the invariants of velocity gradient tensor along fluid trajectories. An alternative approach to coherent structures is shown to lead to their characterization as local maximizers of the largest finite-time Lyapunov exponent field computed directly from particle paths. Both approaches provide effective tools for extracting distinguished Lagrangian structures from three-dimensional velocity data. We illustrate the results on steady and unsteady ABC-type flows.

MSC:
76R99 Diffusion and convection
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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