Abstract-
Rapidly growing instabilities between unequal strength,
counter-rotating vortex pairs are discussed. The vortex pairs are generated in a
towing tank in the wakes of wings with outboard triangular flaps. The
circulation strength ratios of the flap to tip vortex pairs range from -0.4 to
-0.7. The nearly straight vortex filaments first form loops around the stronger
wing tip vortices. The loops soon detach and form rings and move in the wake
under self induction. The subsequent development of the instability makes
quickly the nearly quasi-steady and two-dimensional wakes unsteady and three
dimensional. Velocity, vorticity, and enstrophy measurements in a fixed plane,
in conjuction with the flow observations, are used to quantify the behavior of
the vortex pairs. Once the three-dimensional interactions develop,
two-dimensional kinetic energy and enstrophy drop, and enstrophy dispersion
radius increases sharply. Concurrent analytical and numerical studies are
employed to explain this behavior of the vortex wake. The analyses of Crow
(1970) and Widnall(1974) are extended, where planar perturbations are
destabilized in the straining field is able to overcome rotational effects, now
due not only to self-induction, but also to the orbital motion of a vortex pair.
The effect of the presence of a second symmetric vortex pair on the stability of
a single pair is examined by extending Crouch's (1997) analysis of co-rotating
symmetric pairs. Results from a spectral Navier-Stokes initial value code with
sub-grid scale modeling support the theoretical models in the linear regime and
allow for the computation of the nonlinear evolution of the instabilities. A
pair of co-rotating Gaussian vortices perturbed by noise is seen to give rise to
elliptic instabilities, leading to the formation of vorticity bridges adjoining
the vortices and eventually resulting in the merger of the two. Long-wavelength
perturbations of a counter-rotating pair grow at a rate in agreement with the
linear model, eventually yielding the wrapping and ring-rejection behavior
observed in experiments. This rapid transformation of the wake into a highly
three-dimensional one offers a possible way of alleviating the hazard posed by
the vortex wake of transport aircraft.
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