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Generalized helical vortex pairs

Published online by Cambridge University Press:  20 February 2019

E. Durán Venegas Open the ORCID record for E. Durán Venegas [Opens in a new window]  and
S. Le Dizès Open the ORCID record for S. Le Dizès [Opens in a new window]
E. Durán Venegas*
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, Marseille, France
S. Le Dizès
Affiliation:
Aix Marseille Univ, CNRS, Centrale Marseille, IRPHE, Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

New solutions describing the interaction of helical pairs of counter-rotating vortices are obtained using a vortex filament approach. The vortices are assumed to have a small core size allowing the calculation of the self-induced velocities from the Biot–Savart law using the cutoff theory. These new vortex structures do not possess any helical symmetry but they exhibit a spatial periodicity and are stationary in a rotating and translating frame. Their properties, such as radial deformation, frame velocity and induced flow, are provided as a function of the four geometric parameters characterizing each solution. Approximate solutions are also obtained when the mutual interaction is weak. This allows us to provide explicit expressions for the rotation and translation velocities of the structure in this limit. First-order corrections describing helix deformation are also calculated and used for comparison with the numerical results. The variation of the vortex core size induced by the helix deformation is also analysed. We show that these variations have a weak effect on the shape and characteristics of the solutions, for the range of parameters that we have considered. The results are finally applied to rotor wakes. It is explained how these solutions could possibly describe the far wake of an helicopter rotor in vertical flight.

JFM classification

Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 523 - 545
Copyright
© 2019 Cambridge University Press 

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