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A family of helically symmetric vortex equilibria

Published online by Cambridge University Press:  26 August 2009

DAN LUCAS  and
DAVID G. DRITSCHEL
DAN LUCAS*
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
DAVID G. DRITSCHEL
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
*
†Email address for correspondence: [email protected]
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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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 634 , 10 September 2009 , pp. 245 - 268
Copyright
Copyright © Cambridge University Press 2009

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References

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