Theoretical and Experimental Study of the Stability of a Vortex Pair

Abstract

The linear stability of the trailing vortex pair from an aircraft is discussed. The method of matched asymptotic expansions is used to obtain a general solution for the flow field within and near a curved vortex filament with an arbitrary distribution of swirl and axial velocities. The velocity field induced in the neighborhood of the vortex core by distant portions of the vortex line is calculated for a sinusoidally perturbed vortex filament and for a vortex ring. General expressions for the self-induced motion are given for these two cases. It is shown that the details of the vorticity and axial velocity distributions affect the self-induced motion only through the kinetic energy of the swirl and the axial momentum flux. The presence of axial velocity in the core reduces both the angular velocity of the sinusoidal vortex filament and the speed of the ring. The vortex pair instability is then considered in terms of the more general model for self-induced motion of the sinusoidal vortex. The presence of axial velocity within the core slightly decreases the amplification rate of the instability. Experimental results for the distortion and breakup of a perturbed vortex pair are presented.