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Span effect on the turbulence nature of flow past a circular cylinder

  • Bernat Font Garcia (a1) (a2), Gabriel D. Weymouth (a1), Vinh-Tan Nguyen (a2) and Owen R. Tutty (a1)


Turbulent flow evolution and energy cascades are significantly different in two-dimensional (2-D) and three-dimensional (3-D) flows. Studies have investigated these differences in obstacle-free turbulent flows, but solid boundaries have an important impact on the cross-over from 3-D to 2-D turbulence dynamics. In this work, we investigate the span effect on the turbulence nature of flow past a circular cylinder at $Re=10\,000$ . It is found that even for highly anisotropic geometries, 3-D small-scale structures detach from the walls. Additionally, the natural large-scale rotation of the Kármán vortices rapidly two-dimensionalise those structures if the span is 50 % of the diameter or less. We show this is linked to the span being shorter than the Mode B instability wavelength. The conflicting 3-D small-scale structures and 2-D Kármán vortices result in 2-D and 3-D turbulence dynamics which can coexist at certain locations of the wake depending on the domain geometric anisotropy.


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Adams, N. A. & Hickel, S. 2009 Implicit large-eddy simulation: theory and application. In Advances in Turbulence XII, pp. 743750. Springer.
Bao, Y., Palacios, R., Graham, J. M. R. & Sherwin, S. 2016 Generalized thick strip modelling for vortex-induced vibration of long flexible cylinders. J. Comput. Phys. 321, 10791097.
Bao, Y., Zhu, H. B., Huan, P., Wang, R., Zhou, D., Han, Z. L., Palacios, R., Graham, M. & Sherwin, S. 2019 Numerical prediction of vortex-induced vibration of flexible riser with thick strip method. J. Fluids Struct. (in press).
Batchelor, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids 12 (12), II–233–II–239.
Biancofiore, L. 2014 Crossover between two- and three-dimensional turbulence in spatial mixing layers. J. Fluid Mech. 745, 164179.
Biancofiore, L., Gallaire, F. & Pasquetti, R. 2012 Influence of confinement on obstacle-free turbulent wakes. Comput. Fluids 58, 2744.
Bloor, M. S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19 (2), 290304.
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44, 427451.
Celani, A., Musacchio, S. & Vincenzi, D. 2010 Turbulence in more than two and less than three dimensions. Phys. Rev. Lett. 104 (18), 184506.
Choi, K.-S. & Lumley, J. L. 2001 The return to isotropy of homogeneous turbulence. J. Fluid Mech. 436, 5984.
Chyu, C. & Rockwell, D. 1996 Evolution of patterns of streamwise vorticity in the turbulent near wake of a circular cylinder. J. Fluid Mech. 320, 117137.
Dong, S. & Karniadakis, G. E. 2005 DNS of flow past a stationary and oscillating cylinder at Re = 10 000. J. Fluids Struct. 20, 519531.
Dritschel, D. G., Scott, R. K., Macaskill, C., Gottwald, G. A. & Tran, C. V. 2008 Unifying scaling theory for vortex dynamics in two-dimensional turbulence. Phys. Rev. Lett. 101, 094501.
Gilbert, A. D. 1988 Spiral structures and spectra in two-dimensional turbulence. J. Fluid Mech. 193, 475497.
Hendrickson, K., Weymouth, G. D., Yue, D. K.-P. & Yue Yu, X. 2019 Wake behind a three-dimensional dry transom stern. Part 1: flow structure and large-scale air entrainment. J. Fluid Mech. 875, 854883.
Kourta, A., Boisson, H. C., Chassaing, P. & Ha Minh, H. 1987 Nonlinear interaction and the transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 181, 141161.
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 14171423.
Leith, C. E. 1968 Diffusion approximation for two-dimensional turbulence. Phys. Fluids 11, 671673.
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123176.
Lumley, J. L. & Newman, G. R. 1977 The return to isotropy of homogeneous turbulence. J. Fluid Mech. 82, 161178.
Maertens, A. P. & Weymouth, G. D. 2015 Accurate Cartesian-grid simulations of near-body flows at intermediate Reynolds numbers. Comput. Meth. Appl. Mech. Engng 283, 106129.
Mittal, R. & Balachandar, S. 1995 Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders. Phys. Fluids 7 (8), 18411865.
Noack, B. R. 1999 On the flow around a circular cylinder. Part I: laminar and transitional regime. Z. Angew. Math. Mech. J. Appl. Math. Mech. 79, 223226.
Norberg, C. 2003 Fluctuating lift on a circular cylinder: review and new measurements. J. Fluids Struct. 17, 5796.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Roshko, A.1954 On the development of turbulent wakes from vortex streets. NACA Rep. 1191. National Advisory Committee for Aeronautics, Washington D.C.
Schulmeister, J. C., Dahl, J. M., Weymouth, G. D. & Triantafyllou, M. S. 2017 Flow control with rotating cylinders. J. Fluid Mech. 825, 743763.
Smith, L. M., Chasnov, J. R. & Waleffe, F. 1996 Crossover from two- to three-dimensional turbulence. Phys. Rev. Lett. 77 (12), 24672470.
Weymouth, G. D. & Yue, D. K. P. 2011 Boundary data immersion method for Cartesian-grid simulations of fluid-body interaction problems. J. Comput. Phys. 230, 62336247.
Williamson, C. H. K. 1996a Three-dimensional wake transition. J. Fluid Mech. 328, 345407.
Williamson, C. H. K. 1996b Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.
Xia, H., Byrne, D., Falkovich, G. & Shats, M. 2011 Upscale energy transfer in thick turbulent fluid layers. Nat. Phys. 7, 321324.
Xiao, Z., Wan, M., Chen, S. & Eyink, G. L. 2009 Physical mechanism of the inverse energy cascade of two-dimensional turbulence: a numerical investigation. J. Fluid Mech. 619, 144.
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Span effect on the turbulence nature of flow past a circular cylinder

  • Bernat Font Garcia (a1) (a2), Gabriel D. Weymouth (a1), Vinh-Tan Nguyen (a2) and Owen R. Tutty (a1)


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