Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-25T12:40:48.609Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite-Péclet-number effects on the scaling exponents of high-order passive scalar structure functions

Published online by Cambridge University Press:  26 October 2012

J. Lepore  and
L. Mydlarski
J. Lepore
Affiliation:
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montréal, QC, H3A 0C3, Canada
L. Mydlarski*
Affiliation:
Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montréal, QC, H3A 0C3, Canada
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of scalar-field (temperature) boundary conditions on the inertial-convective-range scaling exponents of the high-order passive scalar structure functions is studied in the turbulent, heated wake downstream of a circular cylinder. The temperature field is generated two ways: using (i) a heating element embedded within the cylinder that generates the hydrodynamic wake (thus creating a heated cylinder) and (ii) a mandoline (an array of fine, heated wires) installed downstream of the cylinder. The hydrodynamic field is independent of the scalar-field boundary conditions/injection methods, and the same in both flows. Using the two heat injection mechanisms outlined above, the inertial-convective-range scaling exponents of the high-order passive scalar structure functions were measured. It is observed that the different scalar-field boundary conditions yield significantly different scaling exponents (with the magnitude of the difference increasing with structure function order). Moreover, the exponents obtained from the mandoline experiment are smaller than the analogous exponents from the heated cylinder experiment (both of which exhibit a significant departure from the Kolmogorov prediction). Since the observed deviation from the Kolmogorov $n/ 3$ prediction arises due to the effects of internal intermittency, the typical interpretation of this result would be that the scalar field downstream of the mandoline is more internally intermittent than that generated by the heated cylinder. However, additional measures of internal intermittency (namely the inertial-convective-range scaling exponents of the mixed, sixth-order, velocity–temperature structure functions and the non-centred autocorrelations of the dissipation rate of scalar variance) suggest that both scalar fields possess similar levels of internal intermittency – a distinctly different conclusion. Examination of the normalized high-order moments reveals that the smaller scaling exponents (of the high-order passive scalar structure functions) obtained for the mandoline experiment arise due to the smaller thermal integral length scale of the flow (i.e. the narrower inertial-convective subrange) and are not solely the result of a more intermittent scalar field. The difference in the passive scalar structure function scaling exponents can therefore be interpreted as an artifact of the different, finite Péclet numbers of the flows under consideration – an effect that is notably less prominent in the other measures of internal intermittency.

JFM classification

Turbulent Flows: Intermittency Turbulent Flows: Turbulent Flows Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 453 - 481
Copyright
©2012 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anselmet, F., Antonia, R. A. & Danaila, L. 2001 Turbulent flows and intermittency in laboratory experiments. Planet. Space Sci. 49, 1177–1191.CrossRefGoogle Scholar
Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.CrossRefGoogle Scholar
Antonia, R. A., Hopfinger, E. J., Gagne, Y. & Anselmet, F. 1984 Temperature structure functions in turbulent shear flows. Phys. Rev. A 30, 2704–2707.Google Scholar
Antonia, R. A., Satyaprakash, B. R. & Chambers, A. J. 1982 Reynolds number dependence of velocity structure functions in turbulent shear flows. Phys. Fluids 25, 29–37.CrossRefGoogle Scholar
Arneodo, A., Baudet, C., Belin, F., Benzi, R., Castaing, B., Chabaud, B., Chavarria, R., Ciliberto, S., Camussi, R., Chillà, F., Dubrulle, B., Gagne, Y., Hebral, B., Herweijer, J., Marchand, M., Maurer, J., Muzy, J. F., Naert, A., Noullez, A., Peinke, J., Roux, F., Tabeling, P., van de Water, W. & Willaime, H. 1996 Structure functions in turbulence, in various flow configurations, at Reynolds number between 30 and 5000, using extended self-similarity. Europhys. Lett. 34, 411.CrossRefGoogle Scholar
Beaulac, S. & Mydlarski, L. 2004 Dependence on the initial conditions of scalar mixing in the turbulent wake of a circular cylinder. Phys. Fluids 16, 3161–3172.Google Scholar
Belin, F., Tabeling, P. & Willaime, H. 1996 Exponents of the structure functions in a low temperature helium experiment. Physica D 93, 52–63.Google Scholar
Benzi, R., Ciliberto, S., Baudet, C. & Ruiz Chavarria, G. 1995 On the scaling of three-dimensional homogeneous and isotropic turbulence. Physica D 80, 385–398.CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. & Succi, S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. E 48, R29–R32.Google Scholar
Berajeklian, A. & Mydlarski, L. 2011 Simultaneous velocity–temperature measurements in the heated wake of a cylinder with implications for the modelling of turbulent passive scalars. Phys. Fluids 23, 055107.CrossRefGoogle Scholar
Boratav, O. N. & Pelz, R. B. 1997 Structures and structure functions in the inertial range of turbulence. Phys. Fluids 9, 1400–1415.Google Scholar
Boratav, O. N. & Pelz, R. B. 1998 Coupling between anomalous velocity and passive scalar increments in turbulence. Phys. Fluids 10, 2122–2124.Google Scholar
Camussi, R. & Verzicco, R. 2000 Anomalous scaling exponents and coherent structures in high Re fluid turbulence. Phys. Fluids 12, 676–687.Google Scholar
Cao, N. & Chen, S. 1997 An intermittency model for passive-scalar turbulence. Phys. Fluids 9, 1203–1205.Google Scholar
Chambers, A. J. & Antonia, R. A. 1984 Atmospheric estimates of power-law exponents $\ensuremath{\mu} $ and ${\ensuremath{\mu} }_{\theta } $ . Boundary-Layer Meteorol. 28 (3–4), 343–352.Google Scholar
Chen, S. & Cao, N. 1997 Anomalous scaling and structure instability in three-dimensional passive scalar turbulence. Phys. Rev. Lett. 78, 3459–3462.Google Scholar
Chen, S. & Kraichnan, R. H. 1998 Simulations of a randomly advected passive scalar field. Phys. Fluids 10, 2867–2884.Google Scholar
Corrsin, S. 1951 On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469–473.Google Scholar
Danaila, L., Anselmet, F., Zhou, T. & Antonia, R. A. 1999 A generalization of Yaglom’s equation which accounts for the large-scale forcing in heated decaying turbulence. J. Fluid Mech. 391, 359–372.CrossRefGoogle Scholar
Danaila, L. & Mydlarski, L. 2001 Effect of gradient production on scalar fluctuations in decaying grid turbulence. Phys. Rev. E 64, 016316.Google Scholar
Dimotakis, P. E. 2005 Turbulent mixing. Annu. Rev. Fluid Mech. 37, 329–356.Google Scholar
Frenkiel, F. N. & Klebanoff, P. S. 1967 Higher-order correlations in a turbulent field. Phys. Fluids 10, 507–520.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Frisch, U., Sulem, P.-L. & Nelkin, M. 1978 A simple dynamical model of intermittent fully developed turbulence. J. Fluid Mech. 87, 719–736.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
Gylfason, A. & Warhaft, Z. 2004 On higher order passive scalar structure functions in grid turbulence. Phys. Fluids 16, 4012–4019.Google Scholar
Holzer, M. & Siggia, E. D. 1994 Turbulent mixing of a passive scalar. Phys. Fluids 6, 1820–1837.Google Scholar
Jayesh, , Tong, C. & Warhaft, Z. 1994 On temperature spectra in grid turbulence. Phys. Fluids 6, 306–312.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
Kraichnan, R. H. 1994 Anomalous scaling of a randomly advected passive scalar. Phys. Rev. Lett. 72, 1016–1019.CrossRefGoogle ScholarPubMed
LaRue, J. C., Deaton, T. & Gibson, C. H. 1975 Measurement of high-frequency turbulent temperature. Rev. Sci. Instrum. 46, 757–764.Google Scholar
Lemay, J. & Benaïssa, A. 2001 Improvement of cold-wire response for measurement of temperature dissipation. Exp. Fluids 31, 347–356.CrossRefGoogle Scholar
Lepore, J. & Mydlarski, L. 2009 Effect of the scalar injection mechanism on passive scalar structure functions in a turbulent flow. Phys. Rev. Lett. 103, 034501.Google Scholar
Lévêque, E., Ruiz-Chavarria, G., Baudet, C. & Ciliberto, S. 1999 Scaling laws for the turbulent mixing of a passive scalar in the wake of a cylinder. Phys. Fluids 11, 1869–1879.CrossRefGoogle Scholar
Lienhard, J. H. & Helland, K. N. 1989 An experimental analysis of fluctuating temperature measurements using hot-wires at different overheats. Exp. Fluids 7, 265–270.Google Scholar
Maurer, J., Tabeling, P. & Zocchi, G. 1994 Statistics of turbulence between two counterrotating disks in low-temperature helium gas. Europhys. Lett. 26, 31–36.CrossRefGoogle Scholar
Meneveau, C., Sreenivasan, K. R., Kailasnath, P. & Fan, M. S. 1990 Joint multifractal measures: theory and applications to turbulence. Phys. Rev. A 41, 894–913.Google Scholar
Mydlarski, L 2003 Mixed velocity-passive scalar statistics in high-Reynolds-number turbulence. J. Fluid Mech. 475, 173–203.Google Scholar
Mydlarski, L. & Warhaft, Z. 1996 On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J. Fluid Mech. 320, 331–368.Google Scholar
Mydlarski, L. & Warhaft, Z. 1998 Passive scalar statistics in high-Péclet-number grid turbulence. J. Fluid Mech. 358, 135–175.Google Scholar
Oboukhov, A. M. 1949 Structure of the temperature field in turbulent flows. Izv. Akad. Nauk. SSSR Geogr. Geofiz 13, 58–69.Google Scholar
Prasad, R. R., Meneveau, C. & Sreenivasan, K. R. 1988 Multifractal nature of the dissipation field of passive scalars in fully turbulent flows. Phys. Rev. Lett. 61 (1), 74–77.Google Scholar
Ruiz Chavarria, G., Baudet, C. & Ciliberto, S. 1995 Extended self-similarity of passive scalars in fully developed turbulence. Europhys. Lett. 32, 319.Google Scholar
Ruiz-Chavarria, G., Baudet, C. & Ciliberto, S. 1996 Scaling laws and dissipation scale of a passive scalar in fully developed turbulence. Physica D 99, 369–380.CrossRefGoogle Scholar
Schmitt, F., Schertzer, D., Lovejoy, S. & Brunet, Y. 1996 Multifractal temperature and flux of temperature variance in fully developed turbulence. Europhys. Lett. 34 (3), 195–200.CrossRefGoogle Scholar
Schumacher, J., Sreenivasan, K. R. & Yeung, P. K. 2003 Derivative moments in turbulent shear flows. Phys. Fluids 15, 84–90.CrossRefGoogle Scholar
She, Z.-S. & Leveque, E. 1994 Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72, 336–339.CrossRefGoogle ScholarPubMed
Shraiman, B. I. & Siggia, E. D. 2000 Scalar turbulence. Nature 405, 639–646.Google Scholar
Sreenivasan, K. R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165–182.Google Scholar
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472.CrossRefGoogle Scholar
Sreenivasan, K. R., Antonia, R. A. & Danh, H. Q. 1977 Temperature dissipation fluctuations in a turbulent boundary layer. Phys. Fluids 20 (8), 1238–1249.Google Scholar
Sreenivasan, K. R. & Kailasnath, P. 1993 An update on the intermittency exponent in turbulence. Phys. Fluids 5, 512–514.Google Scholar
Stolovitzky, G. & Sreenivasan, K. R. 1993 Scaling of structure functions. Phys. Rev. E 48, R33–R36.Google Scholar
Van Atta, C. W. & Chen, W. Y. 1970 Structure functions of turbulence in the atmospheric boundary layer over the ocean. J. Fluid Mech. 44, 145–159.Google Scholar
Van Atta, C. W. & Park, J. 1972 Statistical self-similarity and inertial subrange turbulence. In Statistical Models and Turbulence (ed. Rosenblatt, M. & Van Atta, C. W.), Lecture Notes in Physics, vol. 12 , pp. 402–426. Springer.Google Scholar
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1–20.Google Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.Google Scholar
Warhaft, Z. & Gylfason, A. 2004 Passive scalar fine scale structure: recent results and implications for the velocity field. In Advances in Turbulence X (ed. Andersson, H. I. & Krogstad), P.-A., p. 801 CIMNE.Google Scholar
Warhaft, Z. & Lumley, J. L. 1978 An experimental study of the decay of temperature fluctuations in grid-generated turbulence. J. Fluid Mech. 88, 659–684.Google Scholar
Watanabe, T. & Gotoh, T. 2006 Intermittency in passive scalar turbulence under the uniform mean scalar gradient. Phys. Fluids 18 (5), 058105.Google Scholar
Xu, G, Antonia, R. A. & Rajagopalan, S 2000 Scaling of mixed longitudinal velocity–temperature structure functions. Europhys. Lett. 49 (4), 452–458.Google Scholar
Yaglom, A. M. 1949 On the local structure of a temperature field in a turbulent flow. Dokl. Akad. Nauk SSSR 69, 743–746.Google Scholar
Zukauskas, A. 1972 Heat transfer from tubes in crossflow. In Advances in Heat Transfer (ed. Hartnett, J. P. & Irvine, T. F. Jr), Advances in Heat Transfer , vol. 8. pp. 93–160. Elsevier.Google Scholar