Skip to main content
×
Home
    • Aa
    • Aa

The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake

  • C. H. K. Williamson (a1)
Abstract

The three-dimensional transition of the flow behind a bluff body is studied, with an emphasis placed on the evolution of large-scale structures in the wake. It has previously been found that there are two fundamental modes of three-dimensional vortex shedding in the wake of a circular cylinder (each mode being dependent on the range of Reynolds number), with a spanwise lengthscale of the same order as the primary streamwise wavelength of the vortex street. However. it is shown in the present study that the wake transition also involves the appearance of large-scale spot-like ‘vortex dislocations’, that grow downstream to a size of the order of 10–20 primary wavelengths. Vortex dislocations are generated between spanwise vortex-shedding cells of different frequency. The presence of these dislocations explains the large intermittent velocity irregularities that were originally found by Roshko (1954) and later by Bloor (1964) to characterize transition. The presence of these vortex dislocations in wake transition is largely responsible for the break-up to turbulence of the wake as it travels downstream.

In order to study their evolution in detail, dislocations have been (passively) forced to occur at a local spanwise position with the use of a small ring disturbance. It is found that ‘two-sided’ dislocations are stable in a symmetric in-phase configuration, and that they induce quasi-periodic velocity spectra and (beat) dislocation-frequency oscillations in the near wake. Intrinsic to these dislocations is a mechanism by which they spread rapidly in the spanwise direction, involving helical twisting of the vortices and axial core flows. This is felt to be a fundamental mechanism by which vortices develop large-scale distortions in natural transition. As the wake travels downstream, the energy at the low dislocation frequency decays slowly (in contrast to the rapid decay of other frequencies), leaving the downstream wake dominated by the large dislocation structures. Distinct similarities are found between the periodic forced dislocations and the intermittent dislocations that occur in natural transition. Further similarities of dislocations in different types of flow suggest that vortex or phase dislocations could conceivably be a generic feature of transition in all shear flows.

Copyright
References
Hide All
Albarede, P. 1991 Self-organisation in the three-dimensional wakes of bluff bodies. Thése de Doctorat de l'Universite de Provence, France.
Albarede, P. & Monkewitz, P. 1992 A model for the formation of oblique shedding patterns and ‘chevrons’ in cylinder wakes. Phys. Fluids A 4 744.
Albarede, P., Provansal, M. & Boyer, L. 1990 Modelisation par l'equation de Guinzburg-Landau du sillage tri-dimensionel d'un obstacle allonge. C. R. Acad. Sci. Paris 310, Serie II, 459.
Bearman, P. W. & Szewczyk, A. 1991 Effects of 3-D imposed disturbances on bluff body near wake flows. Presentation at ONR Workshop on Bluff Wake Dynamics, Arizona State University, Tempe, Arizona.
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499.
Bloor, M. S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19, 290.
Browand, F. K. & Ho, C.-M. 1987 Forced unbounded shear flows. Nucl. Phys. B (Proc. Suppl.) 2, 139.
Browand, F. K., Legendre, S. & Taniguchi, P. 1989 A model of vortex pairing induced by defects in mixing layers. Bull. Am. Phys. Soc. 34, 2269.
Browand, F. K. & Prost-Domasky, S. A. 1988 Technique for acoustic excitation of separated shear flows: preliminary results. ASME Winter meeting, Chicago. Illinois.
Browand, F. K. & Prost-Domasky, S. A. 1990 Experiment on pattern evolution in the 2-D mixing layer. In New Trends in Nonlinear Dynamics and Pattern Forming Phenomena (ed. P. Coullet & P. Huerre), p. 159. NATO ASI Series 8. Plenum.
Browand, F. K. & Troutt, T. R. 1980 A note on the spanwise structure in the two-dimensional mixing layer. J. Fluid Mech. 97, 771.
Browand, F. K. & Troutt, T. R. 1985 The turbulent mixing layer: geometry of large vortices. J. Fluid Mech. 158, 489.
Cantwell, B. 1981 Organised motion in turbulent flow. Ann. Rev. Fluid Mech. 13, 457.
Cantwell, B., Coles, D. & Dimotakis P. 1978 Structure and entrainment in the plane of symmetry of a turbulent spot. J. Fluid Mech. 87, 641.
Choi, W. C. & Guezennec, Y. G. 1990 On the asymmetry of structures in turbulent boundary layers.. Phys. Fluids A 2, 628.
Cimbala, J. M. 1984 Large structure in the far wakes of two-dimensional bluff bodies. Ph.D. thesis, Graduate Aeronautical Laboratories, California Institute of Technology.
Cimbala, J. M., Nagib, H. M. & Roshko, A. 1988 Large structure in the far wakes of two-dimensional bluff bodies. J. Fluid Mech. 190, 265.
Coles, D. 1981 Prospects for useful research on coherent structure in turbulent shear flow. Proc. Indian Acad. Sci: Eng. Sci. 4, 111.
Coles, D. & Barker, S. J. 1975 Some remarks on a synthetic turbulent boundary layer. In Turbulent Mixing in Non-reactive and Reactive Flows (ed. S. N. B. Murphy). p. 285. Plenum.
Dallard, T. & Browand, F. K. 1991 Scale transitions at defect sites in the mixing layer: application of the 2-D arc wavelet transform. J. Fluid Mech. (submitted).
Eisenlohr, H. 1986 Investigations of the wake of a plate parallel to the flow with a blunt trailing edge. Diplom. thesis, Berich 3/1986, Max-Planck-Inst fur Stromungsforschung, Gottingen (In German).
Eisenlohr, H. & Eckelmann, H. 1989 Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number.. Phys. Fluids A 1, 189.
Gad-El-Hak, M., Blackwelder, R. F. & Riley, J. J. 1981 On the growth of turbulent regions in laminar boundary layers. J. Fluid Mech. 110, 73.
Gaster, M. 1969 Vortex shedding from slender cones at low Reynolds numbers. J. Fluid Mech. 38, 565.
Gaster, M. 1971 Vortex shedding from circular cylinders at low Reynolds numbers. J. Fluid Mech. 46, 749.
Gerich, D. 1986 Uber die Veranderung der Karmanschen Wirbelstrasse durch Endscheiben an einem Kreiszylinder. Ph.D. thesis, Mitteilungen Nr. 81, Max Planck Institut fur Stromungsforschung, Gottingen.
Gerich, D. 1987 Uber den kontinuierlich arbeitenden Rauchdraht und die Sichtbarmachung eines Ubergangs vom laminaren zum turbulenten Nachlauf. Bericht 104/1987. Max Planck Institut fur Stromungsforschung, Gottingen.
Gerich, D. & Eckelmann, H. 1982 Influence of end plates and free ends on the shedding frequency of circular cylinders. J. Fluid Mech. 122, 109.
Gerrard, J. H. 1978 The wakes of cylindrical bluff bodies at low Reynolds number.. Phil. Trans. R. Soc. Lond. A 288, 351.
Griffin, O. M. 1988 The effects of current shear on vortex shedding. Marine Technology Div. Rep. Naval Research Laboratory.
Hama, F. R. 1957 Three-dimensional vortex pattern behind a circular cylinder. J. Aeronaut. Sci. 24, 156.
Jesperson, D. C. & Levit, D. 1991 Numerical simulation of flow past a tapered cylinder. 29th Aerospace Sciences Meeting. Reno, Nevada, AIAA Paper 910751.
Kim, J. & Moin 1986 The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields. J. Fluid Mech. 162, 339.
Konig, M., Eisenlohr, H., Eckelmann, H. 1990 The fine structure in the. S—Re relationship of the laminar wake of a circular cylinder. Phys. Fluids A 2, 1607.
Leonard, A. 1985 Computing three-dimensional incompressible flows with vortex elements. Ann. Rev Fluid Mech. 17, 523.
Lewis, C. & Gharib, M. 1992 An exploration of the wake three-dimensionalities caused by a local discontinuity in cylinder diameter.. Phys. Fluids A 4, 104.
Lundgren, T. S. & Ashurst, W. T. 1989 Area-varying waves on curved vortex tubes with application to vortex breakdown. J. Fluid Mech. 200, 283.
Maull, D. J. & Young, R. A. 1973 Vortex shedding from bluff bodies in a shear flow. J. Fluid Mech. 60, 401.
Meiburg, E. & Lasheras, J. 1988 Experimental and numerical investigation of the three-dimensional transition in plane wakes. J. Fluid Mech. 190, 1.
Monkewitz, P., Albarede, P. & Clavin, P. 1990 A simple theoretical model for the formation of ‘chevrons’ in the wake of a cylinder. Bull. Am. Phys. Soc. 35, 2320.
Noack, B. N., Ohle, F. & Eckelmann, H. 1991 On cell formation in vortex streets. J. Fluid Mech. 227, 293.
Nygaard, K. J. & Glezer, A. 1990 Core instability of the spanwise vortices in a plane mixing layer.. Phys. Fluids A 2, 461.
Park, D. S. & Redekopp, L. G. 1991 A model for pattern selection in wake flows. Phys. Fluids (submitted).
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173.
Picirillo, P. S. & Van Atta, C. W. 1991 An experimental study of vortex shedding behind a linearly tapered cylinder at low Reynolds number. J. Fluid Mech. (submitted).
Riley, J. J. & Gad-el-Hak, M. 1985 The dynamics of turbulent spots. In Frontiers in Fluid Mechanics (ed. S. H. Davis and J. L. Lumley), p. 123. Springer.
Rockwell, D., Nuzzi, F. & Magness, C. 1991 Period doubling in the wake of a three-dimensional cylinder.. Phys. Fluids A 3, 1477.
Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Rep. 1191.
Sato, H. 1970 An experimental study of non-linear interaction of velocity fluctuations in the transition region of a two-dimensional wake. J. Fluid Mech. 44, 741.
Sato, H. & Kuriki, K. 1961 The mechanism of transition in the wake of a thin flat plate placed parallel to a uniform flow. J. Fluid Mech. 11, 321.
Schubauer, G. B. & Klebanoff, P. S. 1956 Contributions on the mechanics of boundary layer transition. NACA Rep. 1289.
Slaouti, A. & Gerrard, J. H. 1981 An experimental investigation of the end effects on the wake of a circular cylinder towed through water at low Reynolds numbers. J. Fluid Mech. 112, 297.
Van Atta, C., Gharib, M. & Hammache, M. 1988 Three-dimensional structure of ordered and chaotic vortex streets behind circular cylinders at low Reynolds Numbers. Fluid Dyn. Res. 3, 127.
Wei, T. & Smith, C. R. 1986 Secondary vortices in the wake of circular cylinders. J. Fluid Mech. 169, 513.
Williamson, C. H. K. 1988a Defining a universal and continuous Strouhal—Reynolds number relationship for the laminar vortex shedding of a circular cylinder. Phys. Fluids 31, 2742.
Williamson, C. H. K. 1988b The existence of two stages in the transition to three-dimensionality of a cylinder wake. Phys. Fluids 31, 3165.
Williamson, C. H. K. 1989a Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 579.
Williamson, C. H. K. 1989b Generation of periodic vortex dislocations due to a point disturbance in a planar wake.. Phys. Fluids A 1, 1444.
Williamson, C. H. K. 1991a 2-D and 3-D aspects of the wake of a cylinder, and their relation to wake computations. In Proc. Conf. on Vortex Dynamics and Vortex Methods. AMS-SIAM Lectures in Applied Mathematics, vol. 28, p. 719.
Williamson, C. H. K. 1991b Three-dimensional aspects and transition in the wake of a cylinder. In Turbulent Shear Flows 7 (ed. F. Durst & J. Launder), p. 173 Springer.
Williamson, C. H. K. 1991c The formation of spot-like A-structures caused by vortex dislocations in a wake In Proc. 8th Symp. on Turbulent Shear Flows. Technische Universitat, Munich, Germany, September 1991.
Williamson, C. H. K. 1992 The transition to three-dimensionality in the wake of cylinders. J. Fluid Mech. (submitted).
Williams-Stuber, K. & Gharib, M. 1990 Transition from order to chaos in the wake of an airfoil. J. Fluid Mech. 213, 29.
Wygnanski, I., Sokolov, M. & Friedman, D. 1976 On a turbulent ‘spot’ in a laminar boundary layer. J. Fluid Mech. 78, 785.
Yang, R. 1990 Two-dimensional models of pattern formation in free shear flows. Ph.D. thesis, Aerospace Department, University of Southern California.
Yang, R., Huerre, P. & Coullet, P. 1990 A 2-D model of pattern evolution in mixing layers. In New Trends in Nonlinear Dynamics and Pattern Phenomena, (ed. P. Coullet & P. Huerre), p. 171. NATO ASI Series 8, Plenum.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 116 *
Loading metrics...

Abstract views

Total abstract views: 216 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st October 2017. This data will be updated every 24 hours.