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An elliptic type instability of a counter rotating vortex pair of unequal strength was numerically investigated with a linear stability analysis method. The peak growth rates of the unstable modes were predicted. The instability characteristics were found to differ from an equal strength vortex pair, of either co-rotating or counter rotating vortices. This investigation serves as a fundamental model to the flow of two unequal strength vortices, which can be generated from the ends of aerodynamic surfaces of an aircraft, such as wing tips and ailerons. These results provide predictions of the vortex arrangements likely to develop three dimensional instabilities, which is known to promote the dissipation of the underlying vortex structure.   References Batchelor, G. K., An Introduction to Fluid Dynamics , Cambridge University Press, 1967. Crow, S. C., Stability theory for a pair of trailing vortices, AIAA , 8 (12), 2172--2179, 1970. Kelvin, L., Vibratons of a columnar vortex, Phil. Mag. , 10 , 155--168, 1880. Kerswell, R. R., Elliptical instability, Annu. Rev. Fluid Mech. , 34 , 83--113, 2002. doi:10.1146/annurev.fluid.34081701.171829 Lacaze, L., Ryan. K. and Le Dizes, S., Elliptic instability in a strained Batchelor vortex, J. Fluid Mech. , 577 , 345--361, 2007. doi:10.1017/S0022112007004879 Laporte, F. and Corjon, A. Direct numerical simulations of the elliptic instability of a vortex pair, {Phys. Fluids}, 12 (5), 1016--1031, 2000. doi:10.1063/1.870357 Leweke, T. and Williamson, C. H. K., Cooperative elliptic instability of a vortex pair, J. Fluid Mech. , 360 , 85--119, 1998. Le Diz{e}s, S. and Verga, A., Viscous interactions of two co-rotating vortices before merging, J. Fluid Mech. , 467 , 389--410, 2002. doi:10.1017/S0022112002001532 Meunier, P. and Leweke, T., Elliptic instability of a co-rotating vortex pair, J. Fluid Mech. , 533 , 125--159, 2005. doi:10.1017/S0022112005004325 Moore, D. W. and Saffman, P. G., The instability of a straight vortex filament in a strain field, Proc. R. Soc. Lond. A. , 346 , 413--425, 1975. Sheard, G. J., Thompson, M. C. and Hourigan, K., From spheres to circular cylinders: The stability and flow structures of bluff ring wakes, J. Fluid Mech. , 492 , 147--180, 2003. doi:10.1017/S002211200300512 Sheard, G. J., Leweke, T., Thompson, M. C. and Hourigan, K., Flow around an impulsively arrested circular cylinder, Phys. Fluids , 19 (8), 2007, 083601. doi:10.1063/1.2754346 Sheard, G. J. and Ryan, K., Pressure-driven flow past spheres moving in a circular tube, J. Fluid Mech. , 592 , 233--262, 2007. doi:10.1017/S0022112007008543 So, J., Ryan, K. and Sheard, G. J., Interaction of an unequal-strength vortex pair, In Proceedings of the 16th Australasian Fluid Mechanics Conference , Crown Plaza, Gold Coast, Queensland, Australia, 3--7 Dec 2007, 1457-1462. Spalart, P. R., 1998, Airplane trailing vortices, Annu. Rev. Fluid Mech. , 30 , 107--138. Widnall, S. E. and Sullivan, J. P., On the stability of vortex rings, Proc. Roy. Soc. A , 332 , 335--353, 1973. Widnall, S. E., Bliss, D. B. and Tasi, C.-Y., The instability of short waves on a vortex ring, J. Fluid Mech. , 66 , part 1, 35--47, 1974.

Linear stability analysis of a counter rotating vortex pair of unequal strength