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Practical concerns of implementing a finite-time Lyapunov exponent analysis with under-resolved data

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Abstract

Using Lagrangian techniques to find transport barriers in complex, aperiodic flows necessitates a careful consideration of the available dimensional support (3D versus 2D) and temporal resolution of the data to be analyzed, a particular challenge in experimental data acquisition. To illustrate and diagnose the detrimental effects that can manifest in the computed Lagrangian flow maps and Cauchy–Green strain tensor that are calculated as part of most Lagrangian coherent structure analyses, planar finite-time Lyapunov exponent (FTLE) fields are computed from analytically defined, experimentally collected, and numerically simulated velocity fields. The FTLE fields calculated using three-component, three-dimensional velocity information (3D FTLE) are compared with calculations using two-dimensional data considering only the in-plane velocities (2D FTLE), data that are typically gathered during fluid dynamics experiments. In some regions, where the vortex rotation axis is perpendicular to the plane of interest, the 2D FTLE may perform well. However, in regions where the vortex rotation axis has a non-zero component parallel to the plane of interest, whole structures can fail to be captured by the 2D FTLE. A quantitative analysis of the error in the 2D FTLE field as it relates to instantaneous vorticity deviation core angle is conducted using Hill’s spherical vortex and the wake of a bioinspired pitching panel. The effect of decreasing temporal resolution is studied using simulated 3D experiments of a fully turbulent channel flow, where the time resolution of the velocity data is artificially degraded. The resultant 3D FTLE fields progressively worsen with degrading velocity field temporal resolution by the visible elongation of coherent structures in the streamwise direction, indicative of the poorly resolved intermediate velocity fields. This effect can be mitigated with a simple method that invokes Taylor’s frozen eddy hypothesis. Both dimensional support and temporal resolution problems in experimental velocity fields can cause major errors in the resulting FTLE fields. With fundamental understanding about the flow field of interest, such as local vortex orientation or relevant length and time scales, some of the pitfalls may be avoided.

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Acknowledgements

The authors would like to thank Steven Brunton for his contributions and conversations that fed into the content of this paper. This work was supported by the Air Force Office of Scientific Research under AFOSR Award no. FA9550-14-1-0210.

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  1. Matthew P. Rockwood

    Present address: AS&M, WPAFB, Dayton, OH, 45433, USA

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  1. Mechanical and Aerospace Engineering Department, Syracuse University, Syracuse, NY, 13244, USA

    Matthew P. Rockwood, Thomas Loiselle & Melissa A. Green

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  1. Matthew P. Rockwood
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  2. Thomas Loiselle
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Correspondence to Matthew P. Rockwood.

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Rockwood, M.P., Loiselle, T. & Green, M.A. Practical concerns of implementing a finite-time Lyapunov exponent analysis with under-resolved data. Exp Fluids 60, 74 (2019). https://doi.org/10.1007/s00348-018-2658-1

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