Short-wavelength instability of a vortex in a multipolar strain field

The extension of the elliptical instability to a rotational flow with an n-fold symmetry is considered in this Brief Communication. Based on the geometrical optics approach, the short-wavelength stability analysis of the multipolar strained vortex described by the streamfunction (in polar coordinates) Psi(n) = r(2)/2 - (p/n)r(n) cos(n theta) is carried out for n = 3,4,5 and p greater than or equal to 0. Both the growth rate and the wavevector properties of the most unstable wave are computed as a function of the real parameter epsilon(n) = p(2nC/(n-2))((n-2)/2) which characterizes the geometry of the streamline Psi(n) = C. For almost circular flows, i.e., in the small epsilon(n) limit, exact estimates are also obtained by perturbation methods. (C) 1999 American Institute of Physics. [S1070-6631(99)00602-9].