Abstract
Straight vortex filaments are considered with a circular cross section, with zero vorticity outside a given radius
a
, and with a power-law distribution of vorticity within the radius
a
such that the azimuthal velocity varies like
r
β
as a function of the radius
r
. It is shown that the vortices are stable to a two-dimensional disturbance if –1 <
β
< 1 and unstable if
β
> 1. Numerical values are given for the eigenvalue and compared with results obtained from asymptotic analysis in some limiting cases. The behaviour near
β
= 1 is discussed in some detail. Results are found for different values of the mode number
m
, but for each
m
and
β
it was only possible to find a single root or pair of conjugate complex roots.
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