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Motion of a helical vortex

Published online by Cambridge University Press:  11 December 2017

Oscar Velasco Fuentes Open the ORCID record for Oscar Velasco Fuentes [Opens in a new window]
Oscar Velasco Fuentes*
Affiliation:
Departamento de Oceanografía Física, CICESE, Ensenada, B.C. 22860, México
*
†Email address for correspondence: ovelasco@cicese.mx
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Abstract

This paper deals with the motion of a single helical vortex in an unbounded inviscid incompressible fluid. The vortex is an infinite tube whose centreline is a helix and whose cross-section is a small circle where the vorticity is uniform and parallel to the centreline. Ever since Joukowsky (Trudy Otd. Fiz. Nauk Mosk. Obshch. Lyub. Estest., vol. 16, 1912, pp. 1–31) deduced that this vortex translates and rotates steadily without change of form, numerous attempts have been made to compute the velocities. Here, Hardin’s (Phys. Fluids, vol. 25, 1982, pp. 1949–1952) solution for the velocity field is used to find new expressions for the linear and angular velocities of the vortex. The theoretical results are verified by numerically computing the velocity at a single point using the Helmholtz integral and the Rosenhead–Moore approximation to the Biot–Savart law, and by numerically simulating the vortex evolution, under the Euler equations, in a triple-periodic cube. The new formulae are also shown to be more accurate than previous results over the whole range of values of the vortex pitch and cross-section.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex Flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , R1
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Copyright
© 2017 Cambridge University Press 

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