| Reported herein are results concerning a class of three-dimensional instabilities occurring between nearly parallel wake vortices. The problem was studied experimentally, theoretically, and numerically. The experimental data were taken of pairs of co-rotating vortices produced behind a wing in a towing tank. Particle imaging velocimetry and flow visualization revealed the growth of a sinuous disturbance along the axis of each of the vortices in a pair, followed soon thereafter by merger of the two.; A linear instability analysis explains the basic mechanisms responsible for the initial growth of the disturbance. This theory also explains a related instability for the case of a counter-rotating pair. The analysis reveals that planar disturbances on one vortex tend to grow along the extensional axis of the straining field imposed by the other vortex. However, self- and orbit-induced effects tend to prevent instability by rotating the plane of the perturbation through the straining field. For instability, the rotational effects must act in opposite directions. For displacement perturbations, this condition can only occur for a counter-rotating pair. A co-rotating pair, however, can be de-stabilized by shorter-wavelength “elliptic” modes, in which the core and periphery of the vortex are perturbed in opposite directions.; A numerical study of the problem was undertaken using the cylindrical spectral Navier-Stokes solver of Matsushima and Marcus (1997). In addition to confirming the linear analysis for early growth of the instabilities, the code allowed for the computation of their long-term behavior. The growth of the elliptic instability allows the vortices to form bridges between each other, which eventually yields merger of the co-rotating pair. The displacement instability, acting on a counter-rotating pair, yields the ejection of large hoop-like structures, as was first seen experimentally by Ortega (2001).; Thus, a picture emerges of a strain-induced instability which leads to merger of a co-rotating pair and the ejection of large-scale structures from a counter-rotating pair. The fact that this behavior occurs both in a simplified numerical geometry and in actual airfoil wakes suggests that it is relatively robust, and may apply to other flows involving nearly parallel vortices. |
