Skip to main content Accessibility help

Direct numerical simulation of vortex synchronization due to small perturbations

  • S. H. KIM (a1), J. Y. PARK (a2), N. PARK (a3), J. H. BAE (a4) and J. Y. YOO (a1) (a5)...


Direct numerical simulation (DNS) is performed to investigate the vortex synchronization phenomena in the wake behind a circular cylinder at the Reynolds numbers, Re = 220 (mode-A regime) and 360 (mode-B regime). To generate vortex synchronization, a sinusoidal streamwise velocity perturbation, the frequency of which is about twice the natural shedding frequency, is superimposed on the free stream velocity. At Re = 360, vortex synchronization occurs when the perturbation frequency is exactly twice the natural shedding frequency. However, at Re = 220, it does not occur when the same perturbation frequency condition is imposed. Instead, it occurs when the perturbation frequency is near twice the hypothetical two-dimensional laminar vortex shedding frequency as if there were no wake transition at Re = 220.

It is elucidated that, as a result of vortex synchronization, the trajectory of the Kármán vortices and the vortex structure are changed. The Kármán vortices are formed along the mean separating streamline slightly inside the mean wake bubble at Re = 220, but slightly outside at Re = 360. Thus, the Reynolds shear stress force has different contribution to the streamwise force balance of the mean wake bubble depending on the Reynolds numbers: its magnitude is negligible at Re = 220, compared to other force components, while it reverses its sign at Re = 360. More importantly, at Re = 220, the mode-A instability is suppressed into two-dimensional laminar flow with strong Kármań vortices. At Re = 360, the dominant instability mode changes from mode B to mode A.


Corresponding author

Email address for correspondence:


Hide All
Armstrong, B. J., Barnes, F. H. & Grant, I. 1986 The effect of a perturbation on the flow over a bluff cylinder. Phys. Fluids 29, 20952102.
Balachandar, S., Mittal, R. & Najjar, F. M. 1997 Properties of the mean recirculation region in the wakes of two-dimensional bluff bodies. J. Fluid Mech. 351, 167199.
Barbi, C., Favier, D. P., Maresca, C. A. & Telionis, D. P. 1986 Vortex shedding and lock-on of a circular cylinder in oscillatory flow. J. Fluid Mech. 170, 527544.
Beaudan, P. & Moin, P. 1994 Numerical experiments on the flow past a circular cylinder at subcritical Reynolds number. Tech. Rep. TF-62. Thermosciences Division. Department of Mechanical Engineering, Stanford University.
Blaisdell, A., Mansour, N. N. & Reynolds, W. C. 1991 Numerical simulations of compressible homogeneous turbulence. Tech. Rep. TF-50. Thermosciences Division. Dept. of Mechanical Engineering, Stanford University.
Brede, M., Eckelmann, H. & Rockwell, D. 1996 On secondary vortices in the cylinder wake. Phys. Fluids 8, 21172124.
Ekaterinaris, J. A. 1999 Implicit, high-resolution, compact schemes for gas dynamics and aeroacoustics. J. Comput. Phys. 156, 272299.
Fey, U., König, M. & Eckelmann, H. 1998 A new Strouhal–Reynolds-number relationship for the circular cylinder in the range 47 < Re < 2 × 105. Phys. Fluids 10, 1547.
Griffin, O. M. & Hall, M. S. 1991 Review - vortex shedding lock-on and flow control in bluff body wakes. ASME J. Fluids Engng 113, 526537.
Griffin, O. M. & Ramberg, S. E. 1976 Vortex shedding from a cylinder vibrating in line with an incident uniform flow. J. Fluid Mech. 75, 257271.
Henderson, R. D. 1997 Nonlinear dynamics and pattern formation in turbulent wake transition. J. Fluid Mech. 352, 65112.
Jin, B. J., Park, N. & Yoo, J. Y. 2001 Large eddy simulation of boundary layer transition on the axial turbine blade by rotor induced wake. In Proceedings of 2001 ASME Fluids Engineering Division Summer Meeting, FEDSM2001-18195, New Orleans.
Kim, J. & Choi, H. 2005 Distributed forcing of flow over a circular cylinder. Phys. Fulids 17, 033103.
Kim, W., Yoo, J. Y. & Sung, J. 2006 Dynamics of vortex lock-on in a perturbed cylinder wake. Phys. Fluids 18, 074103.
Konstantinidis, E., Balabani, S. & Yianneskis, M. 2003 The effect of flow perturbations on the near wake characteristics of a circular cylinder. J. Fluids Struct. 18, 367386.
Kravchenko, A. G. & Moin, P. 1997 On the effect of numerical errors in large eddy simulations of turbulent flows. J. Comput. Phys. 131, 310322.
Kwon, K. & Choi, H. 1996 Control of laminar vortex shedding behind a circular cylinder using splitter plates. Phys. Fluids 8, 479486.
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 1642.
Miller, G. D. & Williamson, C. H. K. 1994 Control of three-dimensional phase dynamics in a cylinder wake. Exp. Fluids 18, 2635.
Mittal, R. & Balachandar, S. 1997 On the inclusion of three-dimensional effects in simulations of two-dimensional bluff body wake flows. In Proceedings of ASME Fluids Engineering Division Summer Meeting, Vancouver, British Columbia, Canada. Available on CD-ROM only.
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2003 A robust high-order compact method for large eddy simulation. J. Comput. Phys. 191, 392419.
Park, N. & Mahesh, K. 2007 Analysis of numerical errors in large eddy simulation using statistical closure theory. J. Comput. Phys. 222, 194216.
Park, N., Yoo, J. Y. & Choi, H. 2004 Discretization errors in large eddy simulation: on the suitability of centred and upwind-biased compact difference schemes. J. Comput. Phys. 198, 580616.
Persillon, H. & Braza, M. 1998 Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation. J. Fluid Mech. 365, 2388.
Poncet, P. 2002 Vanishing of mode B in the wake behind a rotationally oscillating circular cylinder. Phys. Fluids 14, 20212024.
Poncet, P. 2004 Topological aspects of three-dimensional wakes behind rotary oscillating cylinders. J. Fluid Mech. 517, 2753.
Posdziech, O. & Grundmann, R. 2001 Numerical simulation of the flow around an infinitely long circular cylinder in the transition regime. Theor. Comput. Fluid Dyn. 15, 121141.
Roshko, A. 1993 Perspectives on bluff body aerodynamics. J. Wind Engng Ind. Aerodyn. 49, 79100.
Sung, J. & Yoo, J. Y. 2003 Near-wake vortex motions behind a circular cylinder at low Reynolds number. J. Fluids Struct. 17, 261274.
Tanida, Y., Okajima, A. & Watanabe, Y. 1973 Stability of a circular cylinder oscillating in uniform flow or in a wake. J. Fluid Mech. 61, 769784.
Visbal, M. R. & Gaitonde, D. V. 1999 High-order-accurate methods for complex unsteady subsonic flows. AIAA J. 37, 12311239.
Visbal, M. R. & Rizzetta, D. P. 2002 Large-eddy simulation on curvilinear grids using compact differencing and filtering schemes. ASME J. Fluids Engng 124, 836847.
Williamson, C. H. K. 1987 Three-dimensional transition in the near wake of a cylinder. Bull. Am. Phys. Soc. 32, 2098.
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, 393441.
Williamson, C. H. K. 1996 a Mode A secondary instability in wake transition. Phys. Fulids 8, 16801682.
Williamson, C. H. K. 1996 b Three-dimensional wake transition. J. Fluid Mech. 328, 345407.
Williamson, C. H. K. 1996 c Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.
Williamson, C. H. K. & Roshko, A. 1990 Measurements of base pressure in the wake of a cylinder at low Reynolds numbers. Z. Flugwiss. Weltraumforsch. 14, 3846.
Yoo, J. Y., Kim, S. H. & Bae, J. H. 2006 Suppressed wake transition and vortex lock-on phenomena in a perturbed flow past a circular cylinder. Bull. Am. Phys. Soc. 51 (9), 127.
Yoo, J. Y., Park, J. Y. & Park, N. 2005 Direct numerical simulation of lock-on phenomenon in the wake of a circular cylinder. Bull. Am. Phys. Soc. 50 (9), 235.
You, D., Mittal, R., Wang, M. & Moin, P. 2006 Analysis of stability and accuracy of finite-differencing schemes on a skewed mesh. J. Comput. Phys. 213, 184204.
Zhang, H.-Q., Fey, U. & Noack, B. R. 1995 On the transition of the cylinder wake. Phys. Fluids 7, 779794.
MathJax is a JavaScript display engine for mathematics. For more information see

Direct numerical simulation of vortex synchronization due to small perturbations

  • S. H. KIM (a1), J. Y. PARK (a2), N. PARK (a3), J. H. BAE (a4) and J. Y. YOO (a1) (a5)...


Full text views

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

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.