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A family of helically symmetric vortex equilibria

  • DAN LUCAS (a1) and DAVID G. DRITSCHEL (a1)
Abstract

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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Corresponding author
Email address for correspondence: danl@mcs.st-and.ac.uk
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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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