SHORT-WAVE INSTABILITIES ON A VORTEX PAIR OF UNEQUAL STRENGTH CIRCULATION RATIO

The creation of vortex pairs occurs in a range of industries, including mixing, transport, and plastic moulding. In particular, vortex pairs are observed in the wake of aircraft, and are the cause of a significant hazard in the aviation industry. Instabilities, which grow on vortex pairs, have been shown to lead to rapid diffusion, thus limiting this safety concern. To date research has only considered instabilities growing on a vortex pair where each vortex has the same magnitude of circulation. However in practice it is unusual to have an equal strength vortex pair. This investigation is the first to consider the instability modes that may develop on a Lamb-Oseen vortex pair of arbitrary circulation ratio. We find a significant change in the growth rates of all instability modes reported previously for an equal strength vortex pair. All simulations employ an accurate spectral-element method to discretise the domain coupled with a three-step time splitting scheme. A wide range of instability wavelengths is considered to ensure that all instability modes are captured. By identifying and enhancing the leading instability modes, we are able to enhance the dissipation of the vortex pair. NOMENCLATURE a characteristic vortex radius b vortex separation distance axial axial vorticity 1 circulation of weak vortex 2 circulation of strong vortex r radial dimension kinematic viscosity instability mode growth rate *=tc normalized instability mode growth rate k instability mode wave number u,v,w velocity components p pressure tc time normalization paramete