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An objective definition of a vortex
Abstract
The most widely used definitions of a vortex are not objective: they identify different structures as vortices in frames that rotate relative to each other. Yet a frame-independent vortex definition is essential for rotating flows and for flows with interacting vortices. Here we define a vortex as a set of fluid trajectories along which the strain acceleration tensor is indefinite over directions of zero strain. Physically, this objective criterion identifies vortices as material tubes in which material elements do not align with directions suggested by the strain eigenvectors. We show using examples how this vortex criterion outperforms earlier frame-dependent criteria. As a side result, we also obtain an objective criterion for hyperbolic Lagrangian structures.
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Citations
Cited by
A variational theory of hyperbolic Lagrangian Coherent Structures
Haller, G. (2011) · Physica D: Nonlinear Phenomena · doi:10.1016/j.physd.2010.11.010 · Cited by 406
Self-citationClassifying vortex wakes using neural networks
Colvert, B., Alsalman, M., & Kanso, E. (2018) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/aaa787 · Cited by 95
Gaedtke, M., Hoffmann, T., Reinhardt, V., Thäter, G., Nirschl, H., & Krause, M. J. (2019) · International Journal of Modern Physics C · doi:10.1142/s012918311950013x · Cited by 12
Finite Time Lyapunov Exponent Analysis of Model Predictive Control and Reinforcement Learning
Krishna, K., Brunton, S. L., & Song, Z. (2023) · IEEE Access · doi:10.1109/access.2023.3326424 · Cited by 12
“Moreover, the FTLE has also been used in fluid dynamics applications to compute Lagrangian coherent structures (LCS), which are finite-time analogs of invariant manifolds that mediate the transport of material in unsteady fluid flows [9], [10], [13], [14], [15], [16], [17], [18].”
MethodSecondary vortex dynamics in the cylinder wake during laminar-to-turbulent transition
McClure, J., Pavan, C., & Yarusevych, S. (2019) · Physical Review Fluids · doi:10.1103/physrevfluids.4.124702 · Cited by 12
Metadata
- Authors
- HALLER, G.
- Venue
- Journal of Fluid Mechanics
- Publisher
- Cambridge University Press (CUP)
- Published
- 2005-02-17
- Volume
- 525
- Pages
- 1-26
- ISSN
- 0022-1120 (ISSN-L)
- 1469-7645
- OpenAlex
- W2158082510
- Cited by
- 943
- References
- 0
- FWCI
- 20.87
- Type
- journal article
- Language
- en
- Open access
- closed
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