Abstract
The dynamics of a pair of parallel counter-rotating vortices has been the object of a large number of studies in the last three decades. The continued interest in this flow is, to a great extent, due to its relevance to the problem of aircraft trailing wakes, whose far field is primarily composed of such a pair. Due to their strength and longevity, these vortices can be dangerous to other aircraft that follow, because of the rolling moment they induce. In addition, the counter-rotating vortex pair represents one of the simplest flow configurations for the study of elementary vortex interactions, which can yield useful information for our understanding of the dynamics of more complex transitional and also turbulent flows.
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References
Crow, S.C. (1970) Stability theory for a pair of trailing vortices, AIAA J. 8, 2172–2179.
Devenport, W.J., Zsoldos, J.S. and Vogel, C.M. (1997) The structure and development of a counter-rotating wing-tip vortex pair. J. Fluid Mech. 332, 71–104.
Eliason, B.G., Gartshore, I.S. and Parkinson, G.V. (1975) Wind tunnel investigation of Crow instability. J. Aircraft 12, 985–988.
Kida, S. and Takaoka, M. (1994) Vortex reconnection, Anou. Rev. Fluid Mech. 26, 168.
Klein, R. and Knio, O.M. (1995) Asymptotic vorticity structure and numerical simulation of slender vortex filaments, J. Fluid Mech. 284, 275–231.
Klein, R. and Majda, A.J. (1993) An asymptotic theory for the nonlinear instability of antiparallel pairs of vortex filaments, Phys. Fluids A 5, 369–379.
Klein, R., Majda, A.J. and Damodaran, K. (1995) Simplified equations for the interactions of nearly parallel vortex filaments, J. Fluid Mech. 288, 201–248.
Leweke, T. and Williamson, C.H.K. (1997) Short-wavelength instability of a counter-rotating vortex pair. To appear in J. Fluid Mech.
Leweke, T. and Williamson, C.H.K. (1997) Experimental study of a long-wavelength vortex pair instability. Submitted to J. Fluid Mech.
Lim, T.T and Nickels, T.B. (1996) Vortex rings, in S.I. Green (ed.), Fluid Vortices, Kluwer Academic Publishers, Dordrecht, pp. 95–154.
Liu, H.-T. (1992) Effects of ambient turbulence on the decay of a trailing vortex wake. J. Aircraft 29, 255.
Melander, M.V. and Hussain, F. (1989) Cross-linking of two antiparallel vortex tubes. Phys. Fluids A 1, 633–636.
Miller, G.D. and Williamson, C.H.K. (1997) Dynamics in the far wake of a delta wing. Submitted to J. Fluid Mech.
Moore, D.W. (1972) Finite amplitude waves on aircraft trailing vortices. Aero. Quart. 23, 307–314.
Moore, D.W. and Saffman, P.G. (1973) Axial flow in laminar trailing vortices. Proc. R. Soc. Lond. A 333, 491–508.
North Atlantic Treaty Organization (1996) The Characterization & Modification of Wakes from Lifting Vehicles in Fluids, AGARD Conference Proceedings, No. 584.
Oshima, Y. and Asaka, S. (1977) Interaction of two vortex rings along parallel axes in air. J. Phys. Soc. Japan 42, 708–713.
Robins, R.E. and Delisi, D.P. (1997) Numerical simulations of three-dimensional trailing vortex evolution. AIAA J. 35, 1552–1555.
Sarpkaya, T. 1983 Trailing vortices in homogeneous and density-stratified media. J. Fluid Mech. 136, 85–109.
Shelley, M.J., Meiron, D.I. and Orszag, S.A. (1993) Dynamical aspects of vortex reconnection of perturbed anti-parallel vortex tubes. J. Fluid Mech. 246, 613–652.
Thomas, P.J. and Auerbach, D. (1994) The observation of the simultaneous development of a long-and a short-wave instability mode on a vortex pair. J. Fluid Mech. 265, 289–302.
Van Dyke, M. (1982) An Album of Fluid Motion, Parabolic Press, Stanford.
Widnall, S.E., Bliss, D.B. and Tsai, C.-Y. (1974) The instability of short waves on a vortex ring, J. Fluid Mech. 66, 33–47.
Widnall, S.E., Bliss, D.B. and Zalay, A. (1971) Theoretical and experimental study of the instability of a vortex pair, in J.H. Olsen, A. Goldberg and M. Rogers (eds.), Aircraft Wake Turbulence and its Detection, Plenum Press, New York, pp. 305–338.
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Leweke, T., Williamson, C.H.K. (1998). Long-Wavelength Instability and Reconnection of a Vortex Pair. In: Krause, E., Gersten, K. (eds) IUTAM Symposium on Dynamics of Slender Vortices. Fluid Mechanics and Its Applications, vol 44. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5042-2_19
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DOI: https://doi.org/10.1007/978-94-011-5042-2_19
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