Vortex Flows and Related Numerical Methods II
ESAIM: Proceedings,
Vol. 1, 1996, pp. 565-575
A Numerical and Analytical Study of Vortex Rings With Swirl
Alexander Lifschitz
Mathematics Dept.
University of Illinois
Chicago, IL 60607, USA
W. Henry Suters
Mathematics Dept.
Carson-Newman College
Jefferson City, TN 37760, USA
J. Thomas Beale
Mathematics Dept.
Duke University
Durham, NC 27708, USA
Abstract
We study the growth of disturbances to vortex rings
with swirl, which are exact solutions of the Euler equations of
inviscid flow, using two contrasting methods. The motion of
the perturbed vortex rings can be regarded as a prototype for
the inviscid dynamics of vortex structures in 3D. Exact rings
with swirl are computed as steady, axisymmetric flows
using a variational method. Asymptotic
analysis in the short wave limit, similar
to geometric optics, leads to ordinary differential equations
for perturbations along particle paths. These ODE's can
be solved for the rings of interest, yielding predicted
maximum growth rates for small disturbances.
These rates are compared with the direct simulation
of sample disturbances using a 3D vortex method to calculate the
evolution according to the Euler equations.
Vortex Flows and Related
Numerical Methods II
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