Optimal Pertubation of a Counter-Rotating Vortex Pair

Abstract

In this paper we study the large time and transient linear dynamics of a two-dimensional counter-rotating vortex pair. Following the suggestion of Sipp et al. (Phys. of Fluids, 2000}, it is shown that the dipole is parameterized by its aspect ratio a/b (a is the vortex radius, and b the distance between the vortices). The instability of the dipole is investigated according to the value of the axial wavenumber k. As expected, the classical Crow and Widnall instabilities are recovered. A simple calculation shows that transient energy amplifications are possible in the dipole. Based on that result, the optimal perturbation at the wavelength of the Crow instability is sought. It is found that the best way to quickly induce the Crow instability is to put a perturbation in the region of the symmetry plane of the dipole. Acting this way decreases by a factor 2.5 the characteristic time of the Crow instability.