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Local and global pairing instabilities of two interlaced helical vortices

Published online by Cambridge University Press:  31 January 2019

Hugo Umberto Quaranta ,
Mattias Brynjell-Rahkola Open the ORCID record for Mattias Brynjell-Rahkola [Opens in a new window] ,
Thomas Leweke Open the ORCID record for Thomas Leweke [Opens in a new window]  and
Dan S. Henningson Open the ORCID record for Dan S. Henningson [Opens in a new window]
Hugo Umberto Quaranta
Affiliation:
IRPHE, CNRS, Aix-Marseille Université, Centrale Marseille, 13384 Marseille, France Aerodynamics Department, Airbus Helicopters, 13725 Marignane, France
Mattias Brynjell-Rahkola
Affiliation:
Linné FLOW Centre, Department of Mechanics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Thomas Leweke*
Affiliation:
IRPHE, CNRS, Aix-Marseille Université, Centrale Marseille, 13384 Marseille, France
Dan S. Henningson
Affiliation:
Linné FLOW Centre, Department of Mechanics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: thomas.leweke@univ-amu.fr
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Abstract

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.

JFM classification

Vortex Flows: Vortex Flows Vortex Flows: Vortex instability Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 927 - 955
Copyright
© 2019 Cambridge University Press 

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