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Local and global pairing instabilities of two interlaced helical vortices
Aix Marseille Univ, Cent Marseille, CNRS, IRPHE, F-13384 Marseille, France.;Airbus Helicopters, Aerodynam Dept, F-13725 Marignane, France..
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.ORCID iD: 0000-0001-9446-7477
Aix Marseille Univ, Cent Marseille, CNRS, IRPHE, F-13384 Marseille, France..
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7864-3071
2019 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 863, p. 927-955Article in journal (Refereed) Published
Abstract [en]

We investigate theoretically and experimentally the stability of two interlaced helical vortices with respect to displacement perturbations having wavelengths that are large compared to the size of the vortex cores. First, existing theoretical results are recalled and applied to the present configuration. Various modes of unstable perturbations, involving different phase relationships between the two vortices, are identified and their growth rates are calculated. They lead to a local pairing of neighbouring helix loops, or to a global pairing with one helix expanding and the other one contracting. A relation is established between this instability and the three-dimensional pairing of arrays of straight parallel vortices, and a striking quantitative agreement concerning the growth rates and frequencies is found. This shows that the local pairing of vortices is the driving mechanism behind the instability of the helix system. Second, an experimental study designed to observe these instabilities in a real flow is presented. Two helical vortices are generated by a two-bladed rotor in a water channel and characterised through dye visualisations and particle image velocimetry measurements. Unstable displacement modes are triggered individually, either by varying the rotation frequency of the rotor, or by imposing a small rotor eccentricity. The observed unstable mode structure, and the corresponding growth rates obtained from advanced processing of visualisation sequences, are in good agreement with theoretical predictions. The nonlinear late stages of the instability are also documented experimentally. Whereas local pairing leads to strong deformations and subsequent breakup of the vortices, global pairing results in a leapfrogging phenomenon, which temporarily restores the initial double-helix geometry, in agreement with recent observations from numerical simulations.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2019. Vol. 863, p. 927-955
Keywords [en]
vortex flows, vortex instability, vortex interactions
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-245126DOI: 10.1017/jfm.2018.904ISI: 000458504100001Scopus ID: 2-s2.0-85060944108OAI: oai:DiVA.org:kth-245126DiVA, id: diva2:1296432
Note

QC 20190315

Available from: 2019-03-15 Created: 2019-03-15 Last updated: 2019-06-11Bibliographically approved

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Brynjell-Rahkola, MattiasHenningson, Dan S.

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