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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ali, Mohamed and Abid, Malek 2014. Self-similar behaviour of a rotor wake vortex core. Journal of Fluid Mechanics, Vol. 740,

    Delbende, Ivan Piton, Benjamin and Rossi, Maurice 2015. Merging of two helical vortices. European Journal of Mechanics - B/Fluids, Vol. 49, p. 363.

    ANDERSEN, MORTEN and BRØNS, MORTEN 2014. Topology of helical fluid flow. European Journal of Applied Mathematics, Vol. 25, Issue. 03, p. 375.

    Delbende, Ivan Rossi, Maurice and Daube, Olivier 2012. DNS of flows with helical symmetry. Theoretical and Computational Fluid Dynamics, Vol. 26, Issue. 1-4, p. 141.

    Hattori, Yuji and Fukumoto, Yasuhide 2014. Modal stability analysis of a helical vortex tube with axial flow. Journal of Fluid Mechanics, Vol. 738, p. 222.

  • Journal of Fluid Mechanics, Volume 634
  • September 2009, pp. 245-268

A family of helically symmetric vortex equilibria

  • DAN LUCAS (a1) and DAVID G. DRITSCHEL (a1)
  • DOI:
  • Published online: 10 September 2009

We present a family of steadily rotating equilibrium states consisting of helically symmetric vortices in an incompressible inviscid irrotational unbounded fluid. These vortices are described by contours bounding regions of uniform axial vorticity. Helical symmetry implies material conservation of axial vorticity (in the absolute frame of reference) when the flow field parallel to vortex lines is proportional to (1+ϵ2r2)−1/2, where ϵ is the pitch and r is the distance from the axis. This material conservation property enables equilibria to be calculated simply by a restriction on the helical stream function. The states are parameterized by their mean radius and centroid position. In the case of a single vortex, parameter space cannot be fully filled by our numerical approach. We conjecture multiply connected contours will characterize equilibria where the algorithm fails. We also consider multiple vortices, evenly azimuthally spaced about the origin. Stability properties are investigated numerically using a helical CASL algorithm.

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D. G. Dritschel 1988 Contour surgery: a topological reconnection scheme for extended integrations using contour dynamics. J. Comput. Phys. 77 (1), 240266.

D. G. Dritschel & M. H. P. Ambaum 1997 A contour-advective semi-Lagrangian algorithm for the simulation of fine-scale conservative fields. Q. J. R. Meteorol. Soc. 123, 10971130.

Y. Fukumoto & V. L. Okulov 2005 The velocity field induced by a helical vortex tube. Phys. Fluids 17 (107101).

M. J. Landman 1990 On the generation of helical waves in circular pipe flow. Phys. Fluids A 2, 738747.

T. Loiseleux , J. M. Chomaz & P. Huerre 1998 The effect of swirl on jets and wakes: linear instability of the rankine vortex with axial flow. Phys. Fluids 10, 11201134.

D. W. Moore & P. G. Saffman 1972 The motion of a vortex filament with axial flow. Phil. Trans. R. Soc. Lond. A 272, 403429.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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