Relative fluid stretching and rotation for sparse trajectory observations

As most mathematically justifiable Lagrangian coherent structure detection methods rely on spatial derivatives, their applicability to sparse trajectory data has been limited. For experimental fluid dynamicists and natural scientists working with Lagrangian trajectory data via passive tracers in uns...

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Bibliographic Details
Published in:Journal of fluid mechanics 2024-10, Vol.996, Article A40
Main Authors: Aksamit, Nikolas O., Encinas-Bartos, Alex P., Haller, George, Rival, David E.
Format: Article
Language:English
Subjects:
Algorithms
Buoys
Clustering
Deformation
Fluid flow
JFM Papers
Mathematics
Measurement techniques
Particle tracking
Rotating fluids
Rotation
Sparsity
Spatial data
Stretching
Tracers
Unsteady flow
Velocity
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Summary:As most mathematically justifiable Lagrangian coherent structure detection methods rely on spatial derivatives, their applicability to sparse trajectory data has been limited. For experimental fluid dynamicists and natural scientists working with Lagrangian trajectory data via passive tracers in unsteady flows (e.g. Lagrangian particle tracking or ocean buoys), obtaining material measures of fluid rotation or stretching is an active topic of research. To facilitate frame-indifferent investigations in unsteady and sparsely sampled flows, we present a novel approach to quantify fluid stretching and rotation via relative Lagrangian velocities. This technique provides a formal objective extension of quasi-objective metrics to unsteady flows by accounting for mean flow behaviour. For extremely sparse experimental data, fluid structures may be significantly undersampled and the mean flow behaviour becomes difficult to quantify. We provide a means to maintain the accuracy of our novel sparse flow diagnostics in extremely sparse sampling scenarios, such as ocean buoy data and Lagrangian particle tracking. We use data from multiple numerical and experimental flows to show that our methods can identify structures beyond existing limits of sparse, frame-indifferent diagnostics and exhibit improved interpretability over common frame-dependent diagnostics.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2024.828