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dc.contributor.authorAksamit, Nikolas Olson
dc.date.accessioned2023-08-22T08:40:35Z
dc.date.available2023-08-22T08:40:35Z
dc.date.issued2023-03-10
dc.description.abstractWe introduce maps of Cauchy–Green strain tensor eigenvalues to barycentric coordinates to quantify and visualize the full geometry of three-dimensional deformation in stationary and non-stationary fluid flows. As a natural extension of Lagrangian coherent structure diagnostics, which provide separate scalar fields and a one-dimensional quantification of fluid deformation, our barycentric mapping visualizes the role of all three Cauchy–Green eigenvalues (or rates of stretching) in a single plot through a novel stretching coordinate system. The coordinate system is based on the distance from three distinct limiting states of deformation that correspond with the dimension of the underlying invariant manifolds. One-dimensional axisymmetric deformation (sphere to rod deformation) corresponds to one-dimensional unstable manifolds, two-dimensional axisymmetric deformation (sphere to disk deformation) corresponds to two-dimensional unstable manifolds and the rare three-dimensional isometric case (sphere to sphere translation and rotation) corresponds to shear-free elliptic Lagrangian coherent structures (LCSs). We provide methods to visualize the degree to which fluid deformation approximates these limiting states, and tools to quantify differences between flows based on the compositional geometry of invariant manifolds in the flow. We also develop a simple analogue for bilinearly representing and plotting both rates of stretching and rotation as a single vector. As with other LCS techniques, these diagnostics define frame-indifferent material features in the flow. We provide multiple computed examples of LCS and momentum transport barriers, and show advantages over other coherent structure diagnostics.en_US
dc.identifier.citationAksamit NO. Mapping the shape and dimension of three-dimensional Lagrangian coherent structures and invariant manifolds. Journal of Fluid Mechanics. 2023en_US
dc.identifier.cristinIDFRIDAID 2137363
dc.identifier.doi10.1017/jfm.2023.93
dc.identifier.issn0022-1120
dc.identifier.issn1469-7645
dc.identifier.urihttps://hdl.handle.net/10037/30156
dc.language.isoengen_US
dc.publisherCambrigde University Pressen_US
dc.relation.journalJournal of Fluid Mechanics
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2023 The Author(s)en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0en_US
dc.rightsAttribution 4.0 International (CC BY 4.0)en_US
dc.titleMapping the shape and dimension of three-dimensional Lagrangian coherent structures and invariant manifoldsen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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Attribution 4.0 International (CC BY 4.0)
Except where otherwise noted, this item's license is described as Attribution 4.0 International (CC BY 4.0)