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Generation of large-scale vortex dislocations in a three-dimensional wake-type flow

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Abstract

Numerical study of three-dimensional evolution of wake-type flow and vortex dislocations is performed by using a compact finite diffenence-Fourier spectral method to solve 3-D incompressible Navier-Stokes equations. A local spanwise nonuniformity in momentum defect is imposed on the incoming wake-type flow. The present numerical results have shown that the flow instability leads to three-dimensional vortex streets, whose frequency, phase as well as the strength vary with the span caused by the local nonuniformity. The vortex dislocations are generated in the nonuniform region and the large-scale chain-like vortex linkage structures in the dislocations are shown. The generation and the characteristics of the vortex dislocations are described in detail.

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References

  1. Williamson, C. H. K., Vortex dynamics in the cylinder wake, Annu. Rev. of Fluid Mech., 1996, 28: 477–539.

    Article  MathSciNet  Google Scholar 

  2. Noack, B. R., Eckelmann, H., A global stability analysis of the steady and periodic cylinder wake, J. Fluid Mech., 1994, 270: 297.

    Article  MATH  Google Scholar 

  3. Iing Guocan, Chang Yong, Three-dimensional stahility analysis of the periodic wake behind a circular cylinder by low-dimensional Galerkin method, Acta Mechanica Sinica (in Chinese), 1999, 31: 660.

    Google Scholar 

  4. Barkley, D., Henderson, R. D., Three-dimensional Floquet stability analysis of the wake of a circular cylinder,J. Fluid Mech., 1996, 322: 215.

    Article  MATH  Google Scholar 

  5. Zhang, H. Q., Fey, U., Noack, B. R. et al., On the transition of cylinder wake, Phys. Fluids, 1995, A7(4): 779.

    Article  Google Scholar 

  6. Henderson, R. D., Nonlinear dynamics and pattern formation in turbulent wake transition, J. Fluid Mech., 1997, 352: 65.

    Article  MATH  MathSciNet  Google Scholar 

  7. Persillon, H., Braza, M., Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier-Stokes simulation, J. Fluid Mech., 1998, 365: 23.

    Article  MATH  Google Scholar 

  8. Ling Guocan, Yu Chenwei, Xiong Zhongmin, The nonlinear features of the wake transition behind a circular cylinder, Proceedings of the Third China-Japan Workshop on Turbulent Flows, Beijing, China, 31 Oct.-4 Nov., 1998.

  9. Karniadakis, G. E., Triantafyllou, G. S., Tbree-dimensional dynamics and transition to turbulence in the wake of bluff objects, J. Fluid Mech., 1992, 238: 1.

    Article  MATH  Google Scholar 

  10. Williamson, C. H. K., The natural and forced formation of spot-like ’vortex dislocations’ in the transition of a wake, J. Fluid Mech., 1992, 243: 393.

    Article  Google Scholar 

  11. Roshko, A., On the development of turbulent wakes from vortex streets, NACA Rep., 1954, 119.

  12. Bloor, M.S., The transition to turbulence in the wake of a circular cylinder, J. Fluid Mech., 1964, 19: 290.

    Article  MATH  Google Scholar 

  13. Lewis, C., Gharib, M., An exploration of the wake three-dimensionalities caused by a local discontinuity in cylinder diameter, Phys. Fluids, 1992, A4: 104.

    Google Scholar 

  14. Eisenlohr, H., Eckelmann, H., Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds number, Phys. Fluids, 1989, 1: 189.

    Article  Google Scholar 

  15. Genard, J. H., The three-dimensional structure of the wake of a rircular cylinder, J. Fluid Mech., 1996, 25: 143.

    Google Scholar 

  16. Gaster, M., Vortex shedding from circular cylinder at low Reynolds number, J. Fluid Mech., 1971, 46: 749.

    Article  Google Scholar 

  17. Bearman, P. W., Challenging problems in bluff body wakes, bluff-body wakes, dynamics and instabilities, IUTAM Sympo- sium Gttinged Germany, 1992, 19.

  18. So, A., Maekawa, H., Study of vortex dislocations in the wake of a flat plate with finite thickness, Transactions of the Japan Society of Mechanical Engineers B, 2000, 66: 649.

    Google Scholar 

  19. Browand, F. K., Troutt, T. R., The turbulent mixing layer: geometry of large vortices, J. Fluid Mech., 1985, 158: 489.

    Article  Google Scholar 

  20. Ling Guocan, Xiong Zhongmin, The three dimensional flow features of interaction between two vortex streets, in Pmceedings of the Eighth International Offshore and Polar Engineering Conference, Mont&al, Canada, May 24–29, 1998.

  21. Pocheau, A., Croquette, V., Gal, P. L.., Turbulence in a cylindrical container of Argon near threshold of convection, Phys. Rev. Lett., 1985, 55: 1094.

    Article  Google Scholar 

  22. Noack, B. R., Ohle, F., Eckelmann, H., On the cell formation in vortex streets, J. Fluid Mech., 1991, 227: 293.

    Article  MATH  Google Scholar 

  23. Albarède, R., Provansal, M., Quasi-periodic cylinder wakes and the Ginzburg-Landau model. J. Fluid Mech., 1995, 291: 191.

    Article  MATH  MathSciNet  Google Scholar 

  24. Park, D. S., Redekopp, L. G., Selection principles for spatio-temporal patterns in wake flows, in Proc. IUTAM Symp. on Bluff-body Wake, Dynamics, and Instability, attingen, Sept. 7–11, 1992.

  25. Monkewitz, P. A., Williamson, C. H. K., Miller, G. D.. Phase dynamics of Khan vortices in cylinder wakes, Phys. Fluids, A, 1996, 8: 91.

    Article  MathSciNet  Google Scholar 

  26. Triantafyllou, G. S., Kamiadakis, G. E., Computational reducibility of unsteady viscous flows, Phys. Fluids A, 1990, 2: 653.

    Article  Google Scholar 

  27. Xiong, Z. M., Ling, G. C., Compact finite difference- Fourier spectral method for three dimensional incompressible Navier-Stokes equation, Acta Mechanica Sinica, 1996, 12(4): 296.

    MATH  Google Scholar 

  28. Xiong, Z. M., Ling, G. C., Compact finite difference-Fourier spectral method for the three dimensional incompressible Navier-Stokes equations and application to vortex dislocation, Plenary Lecture, Fifteenth International Conference on Numerical Methods in Fluid Dynamics, June 24–28, 1996, Monterey, CA, USA, Lecture Notes in Physics, LNP, 490.

  29. Kaniadakis, G. E., Israeli, S.A., Onag, S.A., High-order splitting methods for the incompressible Navier-Stokes equa- tions, J. Comput. Phys., 1994, 97: 414.

    Article  Google Scholar 

  30. Lele, S. K., Compact finite difference schemes with spectral-like resolution, J. Comput. Phys., 1992, 103: 16.

    Article  MATH  MathSciNet  Google Scholar 

  31. Nishioka, M., Sato, H., Measurements of velocity distributions in the wake of a circular cylinder at low Reynolds numbers, J. Fluid Mech., 1974, 65: 97.

    Article  Google Scholar 

  32. Jin, G., Braza, M., A nonreflecting outlet boundary condition for incompressible unsteady Navier-Stokes calculation, J. Comput Phys., 1993, 107: 239.

    Article  MATH  Google Scholar 

  33. Gerich, D.. Eckelmann, H., Influence of end plates and free ends on the shedding frequency of circular cylinders, J. Fluids Mech., 1982, 122: 109.

    Article  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, 100080, Beijing, China

    Guocan Ling & Zhongmin Xiong

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  1. Guocan Ling
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  2. Zhongmin Xiong
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Ling, G., Xiong, Z. Generation of large-scale vortex dislocations in a three-dimensional wake-type flow. Sci. China Ser. A-Math. 44, 1585–1595 (2001). https://doi.org/10.1007/BF02880798

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  • DOI: https://doi.org/10.1007/BF02880798

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