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 geome trical optics approach, the short-wavelength stability analysis of the mult ipolar strained vortex described by the streamfunction (in polar coordinate s) Psi(n) = r(2)/2 - (p/n)r(n) cos(n theta) is carried out for n = 3,4,5 an d p greater than or equal to 0. Both the growth rate and the wavevector pro perties of the most unstable wave are computed as a function of the real pa rameter 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 smal l epsilon(n) limit, exact estimates are also obtained by perturbation metho ds. (C) 1999 American Institute of Physics. [S1070-6631(99)00602-9].