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On the peculiar structure of a helical wake vortex behind an inclined prolate spheroid

  • Fengjian Jiang (a1) (a2), Helge I. Andersson (a1), José P. Gallardo (a3) and Valery L. Okulov (a4) (a5)


The self-similarity law for axisymmetric wakes has for the first time been examined and verified in a complex helical vortex in the far part of an asymmetric wake by means of direct numerical simulation (DNS). The helical vortex is the main coherent flow structure in the transitional non-axisymmetric wake behind an inclined 6:1 prolate spheroid at Reynolds number 3000 based on the minor axis. The gradual development of the complex helical vortex structure has been described in detail all the way from its inception at the spheroid and into the far wake. We observed a complex vortex composition in the generation stage, a rare jet-like wake pattern in the near wake and an abrupt change of helical symmetry in the vortex core without an accompanying change in flow topology, i.e. with no recirculation bubble.


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Alekseenko, S. V., Kuibin, P. A. & Okulov, V. L. 2007 Theory of Concentrated Vortices – an Introduction. Springer.
Alekseenko, S. V., Kuibin, P. A., Okulov, V. L. & Shtork, S. I. 1999 Helical vortices in swirl flow. J. Fluid Mech. 382, 195243.
El Khoury, G. K., Andersson, H. I. & Pettersen, B. 2010 Crossflow past a prolate spheroid at Reynolds number of 10 000. J. Fluid Mech. 659, 365374.
Faler, J. H. & Leibovich, S. 1977 Disrupted states of vortex flow and vortex breakdown. Phys. Fluids 20, 13851400.
Gallardo, J. P., Andersson, H. I. & Pettersen, B. 2014 Turbulent wake behind a curved circular cylinder. J. Fluid Mech. 742, 192229.
George, W. K. 1989 The self-preservation of turbulent flows and its relation to initial conditions and coherent structures. In Advances in Turbulence (ed. George, W. K. & Arndt, R. E. A.), pp. 3973. Hemisphere Publishing Corporation.
Jiang, F., Gallardo, J. P. & Andersson, H. I. 2014 The laminar wake behind a 6:1 prolate spheroid at 45° incidence angle. Phys. Fluids 26, 113602.
Jiang, F., Gallardo, J. P., Andersson, H. I. & Zhang, Z. 2015 The transitional wake behind an inclined prolate spheroid. Phys. Fluids 27, 093602.
Johansson, P. B. V. & George, W. K. 2006 The far downstream evolution of the high-reynolds-number axisymmetric wake behind a disk. Part 1. Single-point statistics. J. Fluid Mech. 555, 363386.
Johansson, P. B. V., George, W. K. & Gourlay, M. J. 2003 Equilibrium similarity, effects of initial conditions and local Reynolds number on the axisymmetric wake. Phys. Fluids 15, 603617.
Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10, 221246.
Leibovich, S. 1984 Vortex stability and breakdown: survey and extension. AIAA J. 22, 11921206.
Manhart, M. 2004 A zonal grid algorithm for DNS of turbulent boundary layers. Comput. Fluids 33, 435461.
Martemianov, S. & Okulov, V. L. 2004 On heat transfer enhancement in swirl pipe flows. Intl J. Heat Mass Transfer 47, 23792393.
Okulov, V. L. 1996 The transition from the right helical symmetry to the left symmetry during vortex breakdown. Tech. Phys. Lett. 22, 798800.
Okulov, V. L., Naumov, I. V., Mikkelsen, R. F. & Sørensen, J. N. 2015 Wake effect on a uniform flow behind wind-turbine model. J. Phys.: Conf. Ser. 625, 012011.
Okulov, V. L. & Sørensen, J. N. 2010 Applications of 2D helical vortex dynamics. Theor. Comput. Fluid Dyn. 24, 395401.
Okulov, V. L., Sørensen, J. N. & Voigt, L. K. 2005 Vortex scenario and bubble generation in a cylindrical cavity with rotating top and bottom. Eur. J. Mech. (B/Fluids) 24, 137148.
Peller, N., Le Duc, A., Tremblay, F. & Manhart, M. 2006 High-order stable interpolations for immersed boundary methods. Intl J. Numer. Meth. Fluids 52, 11751193.
Sarpkaya, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45, 545559.
Taylor, Z. J., Liberzon, A., Gurka, R., Holzman, R., Reesbeck, T. & Diez, F. J. 2013 Experiments on the vortex wake of a swimming knifefish. Exp. Fluids 54, 14.
Velte, C. M., Hansen, M. O. L. & Okulov, V. L. 2009 Helical structure of longitudinal vortices embedded in turbulent wall-bounded flow. J. Fluid Mech. 619, 167177.
Velte, C. M., Okulov, V. L. & Hansen, M. O. L. 2011 Alteration of helical vortex core without change in flow topology. Phys. Fluids 23, 051707.
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