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Evolution of patterns of streamwise vorticity in the turbulent near wake of a circular cylinder

Published online by Cambridge University Press:  26 April 2006

C. Chyu  and
D. Rockwell
C. Chyu
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
D. Rockwell
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
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Abstract

High-image-density particle image velocimetry allows characterization of the instantaneous patterns of streamwise vorticity ωx over the cross-section of the near wake of a circular cylinder, and the manner in which they evolve with streamwise distance. Emphasis is on the Reynolds number Re = 10 × 103, for which the Kelvin–Helmholtz (K–H) mode in the separating shear layers has a streamwise wavelength much smaller than that of the Kármán mode. Consequently, the corresponding spanwise wavelength between ωx concentrations increases substantially from its value in the separating shear layer to a larger one in the near wake. This streamwise evolution is defined by spatial correlations of patterns of instantaneous ωx and interpreted with the aid of the quasi-two-dimensional topology of the wake in the base region of the cylinder. The principal features of the phase-averaged topology are foci of the initially formed Kármán vortices and a saddle point between them. Immediately downstream of this saddle, remarkably coherent patterns of ωx concentrations are evident; they have a wavelength approximately equal to the cylinder diameter. Moreover, larger-scale spanwise distortion eventually occurs. This distortion exhibits several modes; the most severe is a nearly discontinuous variation of patterns of ωx.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 320 , 10 August 1996 , pp. 117 - 137
Copyright
© 1996 Cambridge University Press

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References

Bays-Muchmore, B. & Ahmed, A. 1993 On streamwise vortices in turbulent wakes of cylinders. Phys. Fluids A 5, 387–392.Google Scholar
Bell, J. H. & Mehta, R. D. 1992 Measurements of the streamwise vortical structures in a plane mixing layer. J. Fluid Mech. 239, 213–248.Google Scholar
Bernal, L. P. & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.Google Scholar
Bloor, M. S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19, 290–304.Google Scholar
Breidenthal, R. 1981 Structure in turbulent mixing layers in wakes using a chemical reaction. J. Fluid Mech. 109, 1–24.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects in large structures in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Cantwell, B. & Coles, D. 1983 An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder. J. Fluid Mech. 136, 321–374.Google Scholar
Chyu, C.-K. 1995 A study of the near-wake structure for a circular cylinder. PhD Dissertation, Department of Mechanical Engineering and Mechanics, Lehigh University.
Corcos, G. M. & Lin, S. J. 1984 The mixing layer: deterministic models of a turbulent flow. Part 2. The origin of the three-dimensional motion. J. Fluid Mech. 139, 67–95.Google Scholar
Filler, J. R., Marston, P. L. & Mih, W. C. 1991 Response of the shear layer separating from a circular cylinder to small-amplitude rotational oscillations. J. Fluid Mech. 231, 481–499.Google Scholar
Gerrard, J. H. 1978 The wakes of cylindrical bluff body at low Reynolds number. Phil. Trans. R. Soc. Lond. A 228, 351–382.Google Scholar
Hama, F. R. 1957 Three-dimensional vortex pattern behind a circular cylinder. J. Aero. Sci. Feb., 156–158.Google Scholar
Hayakawa, M. & Hussain, F. 1989 Three-dimensionality of organized structures in a plane turbulent wake. J. Fluid Mech. 206, 375–404.Google Scholar
Ho, C. M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365–424.Google Scholar
Huang, L.-S. & Ho, C.-M. 1990 Small scale transition in a plane mixing layer. J. Fluid Mech. 210, 475–500.Google Scholar
Hussain, A. K. M. F. 1986 Coherent structures in turbulence. J. Fluid Mech. 173, 303–356.Google Scholar
Jimenez, J., Cogolos, M. & Bernal, L. P. 1985 A perspective view of the plane mixing layer. J. Fluid Mech. 152, 125–143.Google Scholar
König, M., Eisenlohr, H. & Eckelmann, H. 1993 Visualization of the spanwise cellular structure of the laminar wake of wall-bounded circular cylinders. Phys. Fluids A 4, 869–872.Google Scholar
Konrad, J.-H. 1976 An experimental investigation of mixing in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. Internal Rep. CJIT-8-PU. California Institute of Technology.
Kourta, A., Boisson, H. C., Chassing, P. & Ha Minh, H. 1987 Nonlinear interaction and the transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 81, 141–161.Google Scholar
Lasheras, J. C., Cho, J. S. & Maxworthy, T. 1986 On the origin and evolution of streamwise vortical structure in a plane free-shear layer. J. Fluid Mech. 172, 231–258.Google Scholar
Lashfras, J.-C. & Choi, H. 1988 Three-dimensional instability of a plane free shear layer; an experimental study of the formation and evolution of streamwise vortices. J. Fluid Mech. 189, 53–86.Google Scholar
Lin, J.-C. & Rockwell, D. 1994 Cinematographic system for high-image-density particle image velocimetry. Exps. Fluids 17, 110–118.Google Scholar
Lin, J.-C., Towfighi, J. & Rockwell, D. 1995 Instantaneous structure of near-wake of a circular cylinder: on the effect of Reynolds number. J. Fluid Mech. 9, 409–418.Google Scholar
Lin, J.-C., Vorobieff, P. & Rockwell, D. 1993 Cinematographic system for high-image-density particle image velocimetry. Bull. Am. Phys. Soc., 38, Abs. IG3, 301.Google Scholar
Lin, J.-C., Vorobieff, P. & Rockwell, D. 1995 Three dimensional patterns of streamwise vorticity in the turbulent near-wake of a cylinder. J. Fluids Struc. 9, 231–234.Google Scholar
Lin, J.-C., Vorobieff, P. & Rockwell, D. 1996 Space-time imaging of a near-wake by high-image-density particle image cinematography. Phys. Fluids 8, 555–564.Google Scholar
Mansy, H., Yang, P. M. & Williams, D. R. 1994 Quantitative measurements of three-dimensional structures in the wake of a circular cylinder. J. Fluid Mech. 20, 277–296.Google Scholar
Meinhart, C. D., Prasad, A. K. & Adrian, R. J. 1992 Parallel digital processor system for particle image velocimetry. Proc. Sixth Intl Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, pp. 30.1.1–30.1.6.
Norberg, C. 1993 Pressure forces on a circular cylinder in cross flow. In Bluff-Body Wakes, Dynamics and Instabilities (ed. H. Eckelmann, J. M. R. Graham, P. Huerre & P. A. Monkewitz), Proc. IUTAM Symp., Göttingen, German, Sept. 7–11, 1992, pp. 275–278. Springer.
Norberg, C. 1994 An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. J. Fluid Mech. 258, 287–316.Google Scholar
Rockwell, D. 1993 Quantitative visualization of bluff-body wakes by particle image velocity. In Bluff-Body Wakes, Dynamics and Instabilities (ed. H. Eckelmann, J. M. R. Graham, P. Huerre & P. A. Monkewitz), Proc. IUTAM Symp., Göttingen, Germany, Sept. 7–11, 1992, pp. 263–270. Springer.
Rockwell, D. & Lin, J.-C. 1993 Quantitative interpretation of complex, unsteady flows via high-image-density particle image velocimetry. In Optical Diagnostics in Fluid and Thermal Flow, Proc. SPIE (Intl Soc. Optical Engng), vol. 2005, pp. 490–503.
Rockwell, D., Magness, C., Robinson, O., Towfighi, J., Akin, O., Gu, W. & Corcoran, T. 1992 Instantaneous structure of unsteady separated flows via particle image velocimetry. Rep. PI-1. Fluid Mech. Lab., Dept. Mech. Engng & Mech., Lehigh University.
Rockwell, D., Magness, C., Towfighi, J., Akin, O. & Corcoran, T. 1993 High-image-density particle image velocimetry using laser scanning techniques. Exps. Fluids 14, 181–192.Google Scholar
Roshko, A. 1976 Structure of turbulent shear flows: a new look. AIAA J. 14, 1349–1357.Google Scholar
Sheridan, J., Soria, J., Wu, J. & Welsh, M. C. 1993 The Kelvin—Helmholtz instability of the separated shear layer from a circular cylinder. In Bluff-Body Wakes, Dynamics and Instabilities (ed. H. Eckelmann, J. M. Graham, P. Huerre & P. A. Monkewitz), Proc. IUTAM Symp., Göttingen, Germany, Sept. 7–11, 1992, pp. 115–117. Springer.
Szepessy, S. & Bearman, P. W. 1992 Aspect ratio and end plate effects on vortex shedding from a circular cylinder. J. Fluid Mech. 234, 191–217.Google Scholar
Towfighi, J. & Rockwell, D. 1994 Flow structure from an oscillating nonuniform cylinder: generation of patterned vorticity concentrations. Phys. Fluids. 6, 531–546.Google Scholar
Unal, M. F. & Rockwell, D. 1988 On vortex formation from a cylinder. Part 1. The initial instability. J. Fluid Mech. 190, 491–512.Google Scholar
Wei, T. & Smith, C. R. 1986 Secondary vortices in the wake of circular cylinders. J. Fluid Mech. 169, 513–533.Google Scholar
Williamson, C. H. K. 1988 The existence of two stages in the transition to three-dimensionality of a cylinder wake. Phys. Fluids 31, 3165–3168.Google Scholar
Williamson, C. H. K. 1989 Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 574–627.Google Scholar
Williamson, C. H. K. 1992 The natural and forced formation of spot-like ‘vortex dislocations’ in the transition of a wake. J. Fluid Mech. 243, 393–441.Google Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Ann. Rev. Fluid Mech. 28, 477–539.Google Scholar
Williamson, C. H. K., Wu, J. & Sheridan, J. 1995 Scaling of streamwise vortices in wakes. Phys. Fluids, 7, 2307–2310.Google Scholar
Wu, J., Sheridan, J., Hourigan, K., Welsh, M. C. & Thompson, M. 1994a Longitudinal vortex structures in a cylinder wake. Phys. Fluids 6, 2883–2885.Google Scholar
Wu, J., Sheridan, J., Soria, J. & Welsh, M. C. 1994b An experimental investigation of streamwise vortices in the wake of a bluff body. J. Fluids Struct. 8, 621–635.Google Scholar
Wu, J., Sheridan, J. & Welsh, M. C. 1994c Vortex filament simulation of the longitudinal vortices found in the wake of a bluff body. In Boundary Layer and Free-Shear Flows. ASME FED, vol. 184, pp. 187–194.
Wu, J., Sheridan, J., Welsh, M. C., Hourigan, K., Soria, J. & Thompson, M. 1994d Shear layer vortices and longitudinal vortices in the wake of a circular cylinder. Proc. Int. Colloq. on Jet, Wakes and Shear Layers, Melbourne, Australia, 18-20 April 1994.
Yokoi, Y. & Kamemoto, K. 1992 Initial state of a three-dimensional vortex structure existing in a two-dimensional boundary layer separation flow (observation of laminar boundary layer separation over a circular cylinder by flow visualization. Japanese Soc. Mech. Engng. Int. J. H 35, 189–195.Google Scholar
Yokoi, Y. & Kamemoto, K. 1993 Initial stage of a three-dimensional vortex structure existing in a two-dimensional boundary layer separation flow (visual observation of laminar boundary-layer separation over a circular cylinder from the side of a separated region). Japanese Soc. Mech. Engng Intl J., H 36, 201–206.Google Scholar
Zhang, H.-Q., Fey, U., Noack, B. R., König, M. & Eckelmann, H. 1995 On the transition of the cylinder wake. Phys. Fluids 7, 779–794.Google Scholar
Zhang, H.-Q., Noack, B. R. & Eckelmann, H. 1994 Numerical computation of the 3-D cylinder wake. Max-Planck-Institut für Strömungsforschung Göttingen, Rep. 3/1994.