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Dynamical effect of the total strain induced by the coherent motion on local isotropy in a wake

Published online by Cambridge University Press:  27 February 2013

F. Thiesset ,
L. Danaila  and
R. A. Antonia
F. Thiesset
Affiliation:
CORIA, Avenue de l’Université, BP 12, 76801 Saint Etienne du Rouvray, France
L. Danaila*
Affiliation:
CORIA, Avenue de l’Université, BP 12, 76801 Saint Etienne du Rouvray, France
R. A. Antonia
Affiliation:
School of Engineering, University of Newcastle, Newcastle, NSW 2308, Australia
*
†Email address for correspondence: danaila@coria.fr
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Abstract

We assess the extent to which local isotropy (LI) holds in a wake flow for different initial conditions, which may be geometrical (the shape of the bluff body which creates the wake) and hydrodynamical (the Reynolds number), as a function of the dynamical effects of the large-scale forcing (the mean strain, $ \overline{S} $, combined with the strain induced by the coherent motion, $\tilde {S} $). LI is appraised through either classical kinematic tests or phenomenological approaches. In this respect, we reanalyse existing LI criteria and formulate a new isotropy criterion based on the ratio between the turbulence strain intensity and the total strain ($ \overline{S} + \tilde {S} $). These criteria involve either time-averaged or phase-averaged quantities, thus providing a deeper insight into the dynamical aspect of these flows. They are tested using hot wire data in the intermediate wake of five types of obstacles (a circular cylinder, a square cylinder, a screen cylinder, a normal plate and a screen strip). We show that in the presence of an organized motion, isotropy is not an adequate assumption for the large scales but may be satisfied over a range of scales extending from the smallest dissipative scale up to a scale which depends on the total strain rate that characterizes the flow. The local value of this scale depends on the particular nature of the wake and the phase of the coherent motion. The square cylinder wake is the closest to isotropy whereas the least locally isotropic flow is the screen strip wake. For locations away from the axis, the study is restricted to the circular cylinder only and reveals that LI holds at scales smaller than those that apply at the wake centreline. Arguments based on self-similarity show that in the far wake, the strength of the coherent motion decays at the same rate as that of the turbulent motion. This implies the persistence of the same degree of anisotropy far downstream, independently of the scale at which anisotropy is tested.

JFM classification

Turbulent Flows: Turbulent Flows Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 720 , 10 April 2013 , pp. 393 - 423
Copyright
©2013 Cambridge University Press

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References

Antonia, R. A., Abe, H. & Kawamura, H. 2009 Analogy between velocity and scalar fields in a turbulent channel flow. J. Fluid Mech. 628, 241–268.CrossRefGoogle Scholar
Antonia, R. A., Anselmet, F. & Chambers, A. J. 1986 Assessment of local isotropy using measurements in a turbulent plane jet. J. Fluid Mech. 163, 365–391.Google Scholar
Antonia, R. A. & Kim, J. 1994 A numerical study of local isotropy of turbulence. Phys. Fluids 6, 2, 834–841.CrossRefGoogle 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., Ould-Rouis, M., Anselmet, F. & Zhu, Y. 1997 Analogy between predictions of Kolmogorov and Yaglom. J. Fluid Mech. 332, 395–409.CrossRefGoogle 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
Antonia, R. A, Zhou, T. & Zhu, Y. 1998 Three-component vorticity measurements in a turbulent grid flow. J. Fluid Mech. 374, 29–57.Google Scholar
Antonia, R. A., Zhu, Y. & Shafi, H. S. 1996 Lateral vorticity measurements in a turbulent wake. J. Fluid Mech. 323, 173–200.CrossRefGoogle Scholar
Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.CrossRefGoogle 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
Browne, L. W. B., Antonia, R. A. & Shah, D. A. 1987 Turbulent energy dissipation in a wake. J. Fluid Mech. 179, 307–326.CrossRefGoogle Scholar
Cannon, S., Champagne, F. & Glezer, A. 1993 Observations of large-scale structures in wakes behind axisymmetric bodies. Exp. Fluids 14, 447–450.Google Scholar
Casciola, C. M., Gualtieri, P, Benzi, R. & Piva, R. 2003 Scale-by-scale budget and similarity laws for shear turbulence. J. Fluid Mech. 476, 105–114.CrossRefGoogle Scholar
Champagne, F. H. 1978 The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, 67–108.Google Scholar
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41, 81–139.Google Scholar
Cimbala, J. M., Nagib, H. M. & Roshko, A. 1988 Large structure in the far wake of two-dimensional bluff bodies. J. Fluid Mech. 190, 265–298.CrossRefGoogle Scholar
Corrsin, S. 1958 Local isotropy in turbulent shear flow. Tech. Rep. NACA RM.Google Scholar
Danaila, L., Anselmet, F. & Antonia, R. A. 2001 Turbulent energy scale budget equations in a fully developped chanel flow. J. Fluid Mech. 430, 87–109.Google Scholar
Danaila, L. & Antonia, R. A. 2009 Spectrum of a passive scalar in moderate Reynolds number homogeneous isotropic turbulence. Phys. Fluids 21, 111702–111706.Google Scholar
Danaila, L., Antonia, R. A. & Burattini, P. 2012 Comparison between kinetic energy and passive scalar energy transfer in locally homogeneous isotropic turbulence. Physica D 241, 224–231.CrossRefGoogle Scholar
Durbin, P. A. & Speziale, C. G. 1991 Local anisotropy in strained turbulence at high Reynolds numbers. Trans. ASME: J. Fluids Engng 117, 402–426.Google Scholar
George, W. K. 1989 The self preservation of turbulent flows and its relation to initial conditions and coherent structure. In Advances in Turbulence (ed. George, W. K.). pp. 39–74. Hemisphere.Google Scholar
Gotoh, T., Fukayama, D. & Nakano, T. 2002 Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation. Phys. Fluids 14, 1065–1081.Google Scholar
Gualtieri, P., Casciola, C. M., Benzi, R., Amati, G. & Piva, R. 2002 Scaling laws and intermittency in homogeneous shear flow. Phys. Fluids 14, 583–596.CrossRefGoogle Scholar
Hayakawa, M. & Hussain, A. K. M. F. 1989 Three-dimensionality of organized structures in a plane turbulent wake. J. Fluid Mech. 206, 375–404.Google Scholar
Hierro, J. & Dopazo, C. 2003 Fourth-order statistical moments of the velocity gradient tensor in homogeneous, isotropic turbulence. Phys. Fluids 15, 3434–3442.Google Scholar
Hill, R. J. 2002 Exact second-order structure–function relationships. J. Fluid Mech. 468, 317–326.Google Scholar
Kang, H. S. & Meneveau, C. 2002 Universality of large eddy simulation model parameters across a turbulent wake behind a heated cylinder. J. Turbul. 3, 1–27.Google Scholar
Kim, J. & Antonia, R. A. 1993 Isotropy of the small scales of turbulence at low Reynolds number. J. Fluid Mech. 251, 219–238.Google Scholar
Kolmogorov, A. 1941 Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 125, 15–17.Google Scholar
Kraichnan, R. H. 1971 Inertial-range transfer in two- and three-dimensional turbulence. J. Fluid Mech. 47, 525–535.Google Scholar
Krishnamoorthy, L. V. & Antonia, R. A. 1987 Temperature-dissipation measurements in a turbulent boundary layer. J. Fluid Mech. 176, 265–281.CrossRefGoogle Scholar
Lavoie, P, Burattini, P., Djenidi, L. & Antonia, R. A. 2005 Effect of initial conditions on decaying grid turbulence at low ${R}_{\lambda } $ . Exp. Fluids 39, 865–874.Google Scholar
Matsumura, M. & Antonia, R. A. 1993 Momentum and heat transport in the turbulent intermediate wake of a circular cylinder. J. Fluid Mech. 250, 651–668.Google Scholar
Mestayer, P. 1982 Local isotropy and anisotropy in a high-Reynolds-number turbulent boundary layer. J. Fluid Mech. 125, 475–503.Google Scholar
Monin, A. S. & Yaglom, A. M. 2007 Statistical Fluid Dynamics, Vol. 2. MIT.Google Scholar
Morris, S. C. & Foss, J. F. 2005 Vorticity spectra in high Reynolds number anisotropic turbulence. Phys. Fluids 17, 088102.Google Scholar
Mouri, H. & Hori, A. 2010 Two-point velocity average of turbulence: statistics and their implications. Phys. Fluids 22, 115110.Google Scholar
O’Neil, J. & Meneveau, C. 1997 Subgrid-scale stresses and their modelling in a turbulent plane wake. J. Fluid Mech. 349, 253–293.Google Scholar
Onsager, L. 1949 Statistical hydrodynamics. Nuovo Cimento 6, 279–287.Google Scholar
Ould-Rouis, M., Antonia, R. A, Zhou, Y. & Anselmet, F. 1996 Turbulent pressure structure function. Phys. Rev. Lett. 77, 2222–2226.Google Scholar
Phan-Thien, N. & Antonia, R. A. 1994 Isotropic Cartesian tensors of arbitrary even orders and velocity gradient correlation functions. Phys. Fluids 6, 3818–3823.Google Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organised wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263–288.Google Scholar
Saddoughi, S. G. & Veeravalli, S. V 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.CrossRefGoogle Scholar
Schumacher, J., Sreenivasan, K. R. & Yeung, P. K. 2003 Derivatives moments in turbulent shear flows. Phys. Fluids 15, 84–90.Google Scholar
Shen, X. & Warhaft, Z. 2000 The anisotropy of the small scale structure in high reynolds number ( ${R}_{\lambda } = 1000$ ) turbulent shear flow. Phys. Fluids 12, 2976–2989.Google Scholar
Siggia, E. D. 1981 Invariants for the one-point vorticity and strain rate correlation functions. Phys. Fluids 24, 1934–1936.Google Scholar
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Ann. Rev. Fluid Mech. 29, 435–472.Google Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. 151 (873), 421–444.Google Scholar
Thiesset, F., Danaila, L., Antonia, R. A. & Zhou, T. 2011 Scale-by-scale energy budgets which account for the coherent motion. J. Phys. Conf. Ser. ETC13, Warsaw 318, 052040.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. 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. 1994 Effect of initial conditions on vortices in a turbulent near wake. AIAA J. 32, 1207–1213.Google Scholar
Zhou, Y. & Antonia, R. A. 1995 Memory effects in a turbulent plane wake. Exp. Fluids 19, 112–120.Google Scholar
Zhou, T. & Antonia, R. A. 2000 Reynolds number dependence of the small-scale structure of grid turbulence. J. Fluid Mech. 406, 81–107.Google Scholar