Skip to main content Accessibility help

The turbulent Kármán vortex

  • J. G. Chen (a1) (a2), Y. Zhou (a1) (a2), R. A. Antonia (a3) and T. M. Zhou (a4)


This work focuses on the temperature (passive scalar) and velocity characteristics within a turbulent Kármán vortex using a phase-averaging technique. The vortices are generated by a circular cylinder, and the three components of the fluctuating velocity and vorticity vectors, $u_{i}$ and $\unicode[STIX]{x1D714}_{i}$ ( $i=1,2,3$ ), are simultaneously measured, along with the fluctuating temperature $\unicode[STIX]{x1D703}$ and the temperature gradient vector, at nominally the same spatial point in the plane of mean shear at $x/d=10$ , where $x$ is the streamwise distance from the cylinder axis and $d$ is the cylinder diameter. We believe this is the first time the properties of fluctuating velocity, temperature, vorticity and temperature gradient vectors have been explored simultaneously within the Kármán vortex in detail. The Reynolds number based on $d$ and the free-stream velocity is $2.5\times 10^{3}$ . The phase-averaged distributions of $\unicode[STIX]{x1D703}$ and $u_{i}$ follow closely the Gaussian distribution for $r/d\leqslant 0.2$ ( $r$ is the distance from the vortex centre), but not for $r/d>0.2$ . The collapse of the distributions of the mean-square streamwise derivative of the velocity fluctuations within the Kármán vortex implies that the velocity field within the vortex tends to be more locally isotropic than the flow field outside the vortex. A possible physical explanation is that the large and small scales of velocity and temperature fields are statistically independent of each other near the Kármán vortex centre, but interact vigorously outside the vortex, especially in the saddle region, due to the action of coherent strain rate.


Corresponding author

Email address for correspondence:


Hide All
Antonia, R. A., Chambers, A. J., Britz, D. & Browne, L. 1986 Organized structures in a turbulent plane jet: topology and contribution to momentum and heat transport. J. Fluid Mech. 172, 211229.
Antonia, R. A., Chambers, A. J., Van Atta, C. W., Friehe, C. A. & Helland, K. N. 1978 Skewness of temperature derivative in a heated grid flow. Phys. Fluids 21, 509510.
Antonia, R. A., Djenidi, L. & Danaila, L. 2014 Collapse of the turbulent dissipative range on Kolmogorov scales. Phys. Fluids 26, 045105.
Batchelor, G. K. 1951 Pressure fluctuations in isotropic turbulence. Math. Proc. Camb. Phil. Soc. 47, 359374.
Browne, L., Antonia, R. A. & Shah, D. A. 1987 Turbulent energy dissipation in a wake. J. Fluid Mech. 179, 307326.
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, 321374.
Chen, J. G., Zhou, Y., Antonia, R. A. & Zhou, T. M. 2018 Characteristics of the turbulent energy dissipation rate in a cylinder wake. J. Fluid Mech. 835, 271300.
Chen, J. G., Zhou, Y., Zhou, T. M. & Antonia, R. A. 2016 Three-dimensional vorticity, momentum and heat transport in a turbulent cylinder wake. J. Fluid Mech. 809, 135167.
Cossin, S.1943 Investigation of flow in an axially symmetrical heated jet of air. Tech. Rep. NACA-WR-W-94.
Davidson, P. 2015 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.
Djenidi, L. & Antonia, R. A. 2009 Momentum and heat transport in a three-dimensional transitional wake of a heated square cylinder. J. Fluid Mech. 640, 109129.
Gibson, C. H., Friehe, C. A. & McConnell, S. O. 1977 Structure of sheared turbulent fields. Phys. Fluids 20, S156.
Granger, R. A. 1985 Fluid Mechanics. CBS College Publishing.
Hangan, H. 2018 Large scale physical simulations of 3D, non-stationary and non-Gaussian wind flows with applications to moving/deformable structures. In IUTAM Symposium on Critical Flow Dynamics involving Moving/Deformable Structures with Design Applications, June 18–22, Santorini, Greece.
Hayakawa, M. & Hussain, F. 1989 Three-dimensionality of organized structures in a plane turbulent wake. J. Fluid Mech. 206, 375404.
Holzer, M. & Siggia, E. D. 1994 Turbulent mixing of a passive scalar. Phys. Fluids. 6, 18201837.
Hu, H., Yang, Z., Sarkar, P. & Haan, F. 2011 Characterization of the wind loads and flow fields around a gable-roof building model in tornado-like winds. Exp. Fluids 51, 835851.
Hussain, A. K. M. F. & Hayakawa, M. 1987 Eduction of large-scale organized structures in a turbulent plane wake. J. Fluid Mech. 180, 193229.
Jiménez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 6590.
Kiya, M. & Matsumura, M. 1988 Incoherent turbulence structure in the near wake of a normal plate. J. Fluid Mech. 190, 343356.
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301305.
Landau, L. D. & Lifschitz, E. M. 1987 Fluid Mechanics. Elsevier/Butterworth-Heinemann.
Lefeuvre, N., Thiesset, F., Djenidi, L. & Antonia, R. A. 2014 Statistics of the turbulent kinetic energy dissipation rate and its surrogates in a square cylinder wake flow. Phys. Fluids 26, 095104.
Matsumura, M. & Antonia, R. A. 1993 Momentum and heat transport in the turbulent intermediate wake of a circular cylinder. J. Fluid Mech. 250, 651668.
Mi, J. & Antonia, R. A. 2010 Approach to local axisymmetry in a turbulent cylinder wake. Exp. Fluids 48, 933947.
Pearson, B. R. & Antonia, R. A. 2001 Reynolds-number dependence of turbulent velocity and pressure increments. J. Fluid Mech. 444, 343382.
Pumir, A. 1994 A numerical study of the mixing of a passive scalar in three dimensions in the presence of a mean gradient. Phys. Fluids 6, 21182132.
Shafi, H. S. & Antonia, R. A. 1997 Small-scale characteristics of a turbulent boundary layer over a rough wall. J. Fluid Mech. 342, 263293.
She, Z.-S., Jackson, E. & Orszag, S. A. 1991 Structure and dynamics of homogeneous turbulence: models and simulations. Proc. R. Soc. Math. Phys. Engng Sci. 434, 101124.
Shraiman, B. I. & Siggia, E. D. 2000 Scalar turbulence. Nature 405, 639646.
Sreenivasan, K. R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165182.
Sreenivasan, K. R. & Antonia, R. A. 1977 Skewness of temperature derivatives in turbulent shear flows. Phys. Fluids 20, 19861988.
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Math. Phys. Engng Sci. 151, 421444.
Tong, C. & Warhaft, Z. 1994 On passive scalar derivative statistics in grid turbulence. Phys. Fluids 6, 21652176.
Watanabe, T. & Gotoh, T. 2004 Statistics of a passive scalar in homogeneous turbulence. New J. Phys. 6, 40.
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203240.
Williamson, C. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477539.
Yang, Z., Sarkar, P. & Hu, H. 2011 An experimental study of a high-rise building model in tornado-like winds. J. Fluids Struct. 27, 471486.
Zhou, T., Pearson, B. R. & Antonia, R. A. 2001 Comparison between temporal and spatial transverse velocity increments in a turbulent plane jet. Fluid Dyn. Res. 28, 127138.
Zhou, T., Razali, S. M., Zhou, Y., Chua, L. P. & Cheng, L. 2009 Dependence of the wake on inclination of a stationary cylinder. Exp. Fluids 46, 11251138.
Zhou, T., Zhou, Y., Yiu, M. W. & Chua, L. P. 2003 Three-dimensional vorticity in a turbulent cylinder wake. Exp. Fluids 35, 459471.
Zhou, Y. & Antonia, R. A. 1992 Convection velocity measurements in a cylinder wake. Exp. Fluids 13, 6370.
Zhou, Y. & Antonia, R. A. 1993 A study of turbulent vortices in the near wake of a cylinder. J. Fluid Mech. 253, 643661.
Zhou, Y. & Antonia, R. A. 1994 Critical points in a turbulent near-wake. J. Fluid Mech. 275, 5981.
Zhu, Y. & Antonia, R. A. 1996 Spatial resolution of a 4-X-wire vorticity probe. Meas. Sci. Technol. 7, 14921497.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

The turbulent Kármán vortex

  • J. G. Chen (a1) (a2), Y. Zhou (a1) (a2), R. A. Antonia (a3) and T. M. Zhou (a4)


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