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

Matthew P. Rockwood, Thomas Loiselle, Melissa A Green

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Article number74
JournalExperiments in Fluids
Volume60
Issue number4
DOIs
StatePublished - Apr 1 2019

Fingerprint

exponents
Vortex flow
temporal resolution
vortices
velocity distribution
Channel flow
Fluid dynamics
Vorticity
Tensors
Elongation
Data acquisition
Flow fields
Experiments
planar structures
channel flow
fluid dynamics
wakes
vorticity
quantitative analysis
elongation

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Fluid Flow and Transfer Processes

Cite this

Practical concerns of implementing a finite-time Lyapunov exponent analysis with under-resolved data. / Rockwood, Matthew P.; Loiselle, Thomas; Green, Melissa A.

In: Experiments in Fluids, Vol. 60, No. 4, 74, 01.04.2019.

Research output: Contribution to journalArticle

@article{fdbbcfa571b840b4a31755560deab8e0,
title = "Practical concerns of implementing a finite-time Lyapunov exponent analysis with under-resolved data",
abstract = "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.",
author = "Rockwood, {Matthew P.} and Thomas Loiselle and Green, {Melissa A}",
year = "2019",
month = "4",
day = "1",
doi = "10.1007/s00348-018-2658-1",
language = "English (US)",
volume = "60",
journal = "Experiments in Fluids",
issn = "0723-4864",
publisher = "Springer Verlag",
number = "4",

}

TY - JOUR

T1 - Practical concerns of implementing a finite-time Lyapunov exponent analysis with under-resolved data

AU - Rockwood, Matthew P.

AU - Loiselle, Thomas

AU - Green, Melissa A

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85063634417&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063634417&partnerID=8YFLogxK

U2 - 10.1007/s00348-018-2658-1

DO - 10.1007/s00348-018-2658-1

M3 - Article

VL - 60

JO - Experiments in Fluids

JF - Experiments in Fluids

SN - 0723-4864

IS - 4

M1 - 74

ER -