Short-wavelength instability of a vortex in a multipolar strain field
Résumé
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) Psin = r2/2 – (p/n)rn cos(n theta) is carried out for n = 3,4,5 and p >= 0. Both the growth rate and the wavevector properties of the most unstable wave are computed as a function of the real parameter epsilonn = p(2nC/(n – 2))(n – 2)/2 which characterizes the geometry of the streamline Psin = C. For almost circular flows, i.e., in the small epsilonn limit, exact estimates are also obtained by perturbation methods.