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Complete self-preservation along the axis of a circular cylinder far wake

Published online by Cambridge University Press:  01 December 2015

S. L. Tang ,
R. A. Antonia ,
L. Djenidi  and
Y. Zhou
S. L. Tang
Affiliation:
Institute for Turbulence–Noise–Vibration Interaction and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, PR China School of Engineering, University of Newcastle, NSW 2308, Australia
R. A. Antonia
Affiliation:
School of Engineering, University of Newcastle, NSW 2308, Australia
L. Djenidi*
Affiliation:
School of Engineering, University of Newcastle, NSW 2308, Australia
Y. Zhou
Affiliation:
Institute for Turbulence–Noise–Vibration Interaction and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, PR China
*
†Email address for correspondence: [email protected]
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Abstract

Self-preservation (SP) analyses are applied to the mean momentum and the scale-by-scale energy budget equations in the far wake of a circular cylinder. The scale-by-scale SP analysis, which is a two-point analysis, complements the SP analysis of the mean momentum equation. Power-law variations are derived for different length scales (e.g. the Taylor microscale and the Kolmogorov length scale) and velocity scales (e.g. the root mean square and the Kolmogorov velocity scale). Further, the SP solutions for the scale-by-scale energy budget equation are exploited to develop an exact relation to estimate the mean turbulent kinetic energy dissipation rate $\bar{{\it\epsilon}}$ on the wake axis. These SP solutions and the new $\bar{{\it\epsilon}}$ relation are well supported by hot-wire data in the far wake at a Reynolds number of 2000 based on the free stream velocity and the cylinder diameter. On the far-wake axis, both the energy spectra and the structure functions exhibit an almost perfect collapse over all wavenumbers and separations, irrespective of the set of scaling variables used for normalisation. This is consistent with a complete self-preservation (i.e. SP is satisfied at all scales of motion) in the far wake.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent Flows Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 786 , 10 January 2016 , pp. 253 - 274
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Copyright
© 2015 Cambridge University Press 

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References

Abe, H., Antonia, R. A. & Kawamura, H. 2009 Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow. J. Fluid Mech. 627, 1–32.Google Scholar
Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 Higher-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.Google Scholar
Antonia, R. A. & Browne, L. W. 1986 Anisotropy of temperature dissipation in a turbulent wake. J. Fluid Mech. 163, 393–403.Google Scholar
Antonia, R. A., Browne, L. W. B., Bisset, D. K. & Fulachier, L. 1987 A description of the organized motion in the turbulent far wake of a cylinder at low Reynolds number. J. Fluid Mech. 184, 423–444.Google Scholar
Antonia, R. A., Browne, L. W. B. & Shah, D. A. 1988 Characteristics of vorticity fluctuations in a turbulent wake. J. Fluid Mech. 189, 349–365.CrossRefGoogle Scholar
Antonia, R. A., Djenidi, L. & Danaila, L. 2014 Collapse of the turbulent dissipation range on Kolmogorov scales. Phys. Fluids 26, 045105.Google Scholar
Antonia, R. A. & Mi, J. 1998 Approach towards self-preservation of turbulent cylinder and screen wakes. Exp. Therm. Fluid Sci. 17, 277–284.Google Scholar
Antonia, R. A., Zhou, T. & Romano, G. P. 2002 Small-scale turbulence characteristics of two-dimensional bluff body wakes. J. Fluid Mech. 459, 67–92.Google Scholar
Aronson, D. & Lofdahl, L. 1993 The plane wake of a cylinder: measurements and inferences on turbulence modeling. Phys. Fluids 5, 1433–1437.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1947 Decay of vorticity in isotropic turbulence. Proc. R. Soc. Lond. A 190, 534–550.Google Scholar
Bisset, D. K., Antonia, R. A. & Britz, D. 1990a Structure of large-scale vorticity in a turbulent far wake. J. Fluid Mech. 218, 463–482.Google Scholar
Bisset, D. K., Antonia, R. A. & Browne, L. W. B. 1990b Spatial organization of large structures in the turbulent far wake of a cylinder. J. Fluid Mech. 218, 439–461.CrossRefGoogle Scholar
Brown, G. L. & Roshko, A. 2012 Turbulent shear layers and wakes. J. Turbul. 13, 1–32.Google Scholar
Browne, L. W., Antonia, R. A. & Shah, D. A. 1987 Turbulent energy dissipation in a wake. J. Fluid Mech. 179, 307–326.Google Scholar
Browne, L. W. B. & Antonia, R. A. 1986 Reynolds shear stress and heat flux measurements in a cylinder wake. Phys. Fluids 29, 709–713.Google Scholar
Burattini, P., Antonia, R. A. & Danaila, L. 2005 Similarity in the far field of a turbulent round jet. Phys. Fluids 17, 025101.CrossRefGoogle Scholar
Camussi, R. & Guj, G. 1995 Experimental analysis of scaling laws in low and moderate Re grid generated turbulence. Exp. Fluids 24, 63–67.Google Scholar
Danaila, L., Anselmet, F., Zhou, T. & Antonia, R. A. 2001 Turbulent energy scale budget equations in a fully developed channel flow. J. Fluid Mech. 430, 87–109.Google Scholar
Djenidi, L. & Antonia, R. A. 2012 A spectral chart method for estimating the mean turbulent kinetic energy dissipation rate. Exp. Fluids 53, 1005–1013.CrossRefGoogle Scholar
Djenidi, L. & Antonia, R. A. 2015 A general self-preservation analysis for decaying homogeneous isotropic turbulence. J. Fluid Mech. 773, 345–365.Google Scholar
Ewing, D., George, W. K., Rogers, M. M. & Moser, R. D. 2007 Two-point similarity in temporally evolving plane wakes. J. Fluid Mech. 577, 287–307.Google Scholar
George, W. K. 1989 The self-preservation of the turbulent flows and its relation to initial conditions and coherent structures. In Advances in Turbulence (ed. George, W. K. & Arndt, R.), pp. 39–74. Springer.Google Scholar
George, W. K. 2012 Asymptotic effect of initial and upstream conditions on turbulence. Trans. ASME J. Fluids Engng 134, 061203.Google Scholar
Hao, Z., Zhou, T., Chua, L. P. & Yu, S. C. M. 2008 Approximations to energy and temperature dissipation rates in the far field of a cylinder wake. Exp. Therm. Fluid Sci. 32, 791–799.CrossRefGoogle Scholar
Kolmogorov, A. 1941 Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 125, 15–17.Google Scholar
Lefeuvre, N., Djenid, L., Antonia, R. A. & Zhou, T. 2014 Turbulent kinetic energy and temperature variance budgets in the far-wake generated by a circular cylinder. In Proceedings 19th Australasian Fluid Mechanics Conference, Melbourne, Australia.Google Scholar
Mi, J., Zhou, Y. & Nathan, G. J. 2004 The effect of Reynolds number on the passive scalar field in the turbulent wake of a circular cylinder. Flow Turbul. Combust. 72, 311–331.CrossRefGoogle Scholar
Sreenivasan, K. R. 1981 Evolution of the centerline probability density function of temperature in a plane turbulent wake. Phys. Fluids 24, 1232–1234.Google Scholar
Thiesset, F., Antonia, R. A. & Djenidi, L. 2014 Consequences of self-preservation on the axis of a turbulent round jet. J. Fluid Mech. 748, R2.Google Scholar
Townsend, A. A. 1951 On the fine-scale structure of turbulence. Proc. R. Soc. Lond. A 208, 534–542.Google Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow, 1st edn. Cambridge University Press.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Wygnanski, I., Champagne, F. & Marasli, B. 1986 On the large-scale structures in two-dimensional, small-deficit, turbulent wakes. J. Fluid Mech. 168, 31–71.Google Scholar
Zhou, Y. & Antonia, R. A. 1995 Memory effects in a turbulent plane wake. Exp. Fluids 19, 112–120.Google Scholar
Zhou, Y., Antonia, R. A. & Tsang, W. K. 1998 The effect of Reynolds number on a turbulent far-wake. Exp. Fluids 25, 118–125.Google Scholar