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Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

Published online by Cambridge University Press:  22 June 2016

A. Briard ,
T. Gomez  and
C. Cambon
A. Briard
Affiliation:
$\partial$’Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris CEDEX 5, France
T. Gomez*
Affiliation:
USTL, LML, 59650 Villeneuve d’Ascq, France Université Lille Nord de France, F-59000 Lille, France
C. Cambon
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, Ecole Centrale de Lyon, 69134 Écully, France
*
†Email address for correspondence: [email protected]
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Abstract

The present work aims at developing a spectral model for a passive scalar field and its associated scalar flux in homogeneous anisotropic turbulence. This is achieved using the paradigm of eddy-damped quasi-normal Markovian (EDQNM) closure extended to anisotropic flows. In order to assess the validity of this approach, the model is compared to several detailed direct numerical simulations (DNS) and experiments of shear-driven flows and isotropic turbulence with a mean scalar gradient at moderate Reynolds numbers. This anisotropic modelling is then used to investigate the passive scalar dynamics at very high Reynolds numbers. In the framework of homogeneous isotropic turbulence submitted to a mean scalar gradient, decay and growth exponents for the cospectrum and scalar energies are obtained analytically and assessed numerically thanks to EDQNM closure. With the additional presence of a mean shear, the scaling of the scalar flux and passive scalar spectra in the inertial range are investigated and confirm recent theoretical predictions. Finally, it is found that, in shear-driven flows, the small scales of the scalar second-order moments progressively return to isotropy when the Reynolds number increases.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Turbulence modelling Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 799 , 25 July 2016 , pp. 159 - 199
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Copyright
© 2016 Cambridge University Press 

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References

Bos, W. J. T. 2014 On the anisotropy of the turbulent passive scalar in the presence of a mean scalar gradient. J. Fluid Mech. 744, 38–64.Google Scholar
Bos, W. J. T. & Bertoglio, J.-P. 2007 Inertial range scaling of scalar flux spectra in uniformly sheared turbulence. Phys. Fluids 19, 025104.CrossRefGoogle Scholar
Bos, W. J. T., Touil, H. & Bertoglio, J.-P. 2005 Reynolds number dependency of the scalar flux spectrum in isotropic turbulence with a uniform scalar gradient. Phys. Fluids 17, 125108.CrossRefGoogle Scholar
Bos, W. J. T., Touil, H., Shao, L. & Bertoglio, J.-P. 2004 On the behavior of the velocity–scalar cross correlation spectrum in the inertial range. Phys. Fluids 16, 3818.CrossRefGoogle Scholar
Brethouwer, G. 2005 The effect of rotation on rapidly sheared homogeneous turbulence and passive scalar transport. Linear theory and direct numerical simulation. J. Fluid Mech. 542, 305–342.CrossRefGoogle Scholar
Briard, A., Gomez, T., Mons, V. & Sagaut, P. 2016 Decay and growth laws in homogeneous shear turbulence. J. Turbul. 17 (7), 699–726.CrossRefGoogle Scholar
Briard, A., Gomez, T., Sagaut, P. & Memari, S. 2015 Passive scalar decay laws in isotropic turbulence: Prandtl number effects. J. Fluid Mech. 784, 274–303.Google Scholar
Burlot, A., Gréa, B.-J., Godeferd, F. S., Cambon, C. & Griffond, J. 2015 Spectral modelling of high Reynolds number unstably stratified homogeneous turbulence. J. Fluid Mech. 765, 17–44.CrossRefGoogle Scholar
Cambon, C. & Jacquin, L. 1989 Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295–317.Google Scholar
Cambon, C., Jeandel, J. & Mathieu, J. 1981 Spectral modelling of homogeneous non-isotropic turbulence. J. Fluid Mech. 104, 247–262.Google Scholar
Cambon, C. & Rubinstein, R. 2006 Anisotropic developments for homogeneous shear flows. Phys. Fluids 18.CrossRefGoogle Scholar
Chasnov, J. R. 1995 Similarity states of passive scalar transport in buoyancy-generated turbulence. Phys. Fluids 7 (6), 1498–1506.CrossRefGoogle Scholar
Comte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of a grid generated turbulence. J. Fluid Mech. 25, 657–682.Google Scholar
Corrsin, S.1958 On local isotropy in turbulent shear flow. NACA RM 58B11.Google Scholar
Danaila, L., Le Gal, P., Anselmet, F., Plaza, F. & Pinton, J. F. 1999 Some new features of the passive scalar mixing in a turbulent flow. Phys. Fluids 11, 636–646.CrossRefGoogle Scholar
De Marinis, D., Chibbaro, S., Meldi, M. & Sagaut, P. 2013 Temperature dynamics in decaying isotropic turbulence with Joule heat production. J. Fluid Mech. 724, 425–449.CrossRefGoogle Scholar
De Souza, F. A., Nguyen, V. D. & Tavoularis, S. 1995 The structure of highly sheared turbulence. J. Fluid Mech. 303, 155–167.Google Scholar
Ferchihi, M. & Tavoularis, S. 2002 Scalar probability density function and fine structure in uniformly sheared turbulence. J. Fluid Mech. 461, 155–182.Google Scholar
Garg, S. & Warhaft, Z. 1998 On the small scale structure of simple shear flow. Phys. Fluids 10, 662–673.CrossRefGoogle Scholar
Gomez, T., Politano, H. & Pouquet, A. 2000 Exact relationship for third-order structure functions in helical flows. Phys. Rev. E 61 (5), 5321–5325.Google ScholarPubMed
Gonzalez, M. 2000 Asymptotic evolution of a passive scalar advected by homogeneous turbulent shear flow. Intl J. Heat Mass Transfer 43, 387–397.Google Scholar
Gylfason, A. & Warhaft, Z. 2009 Effects of axisymmetric strain on a passive scalar field: modelling and experiment. J. Fluid Mech. 628, 339–356.CrossRefGoogle Scholar
Herr, S., Wang, L.-P. & Collins, L. R. 1996 EDQNM model of a passive scalar with a uniform mean gradient. Phys. Fluids 8, 1588.Google Scholar
Herring, J. R., Schertzer, D., Lesieur, M., Newman, G. R., Chollet, J. P. & Larcheveque, M. 1982 A comparative assessment of spectral closures as applied to passive scalar diffusion. J. Fluid Mech. 124, 411–437.CrossRefGoogle Scholar
Jayesh,  & Warhaft, Z. 1992 Probability distribution, conditional dissipation, and transport of passive temperature fluctuations in grid-generated turbulence. Phys. Fluids A 4.Google Scholar
Kader, B. A. & Yaglom, A. M. 1991 Spectra and correlation functions of surface layer atmospheric turbulence in unstable thermal stratification. In Fluid Mechanics and its Applications (ed. Metais, O. & Lesieur, M.), pp. 387–412. Springer.Google Scholar
Karnik, U. & Tavoularis, S. 1989 Measurements of heat diffusion from a continuous line source in a uniformly sheared turbulent flow. J. Fluid Mech. 202, 233–261.CrossRefGoogle Scholar
Kassinos, S. C., Knaepen, B. & Carati, D. 2007 The transport of a passive scalar in magnetohydrodynamic turbulence subjected to mean shear and frame rotation. Phys. Fluids 19, 015105.Google Scholar
Knaus, R. & Pantano, C. 2009 On the effect of heat release in turbulence spectra of non-premixed reacting shear layers. J. Fluid Mech. 626, 67–109.CrossRefGoogle 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).Google Scholar
Leith, C. E. 1971 Atmospheric predictability and two-dimensional turbulence. J. Atmos. Sci. 28, 145–161.2.0.CO;2>CrossRefGoogle Scholar
Lesieur, M. 2008 Turbulence in Fluids, 4th edn. Springer.Google Scholar
Lumley, J. L. 1967 Similarity and the turbulent energy spectrum. Phys. Fluids 10 (4), 855–858.CrossRefGoogle Scholar
Meyers, J. & Meneveau, C. 2008 A functional form of the energy spectrum parametrizing bottleneck and intermittency effects. Phys. Fluids 20, 065109.Google Scholar
Mons, V., Cambon, C. & Sagaut, P. 2016 A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically-averaged descriptors. J. Fluid Mech. 788, 147–182.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. 1998 Passive scalar statistics in high-Péclet-number grid turbulence. J. Fluid Mech. 358, 135–175.Google Scholar
O’Gorman, P. A. & Pullin, D. I. 2003 The velocity–scalar cross spectrum of stretched spiral vortices. Phys. Fluids 15, 280.CrossRefGoogle Scholar
O’Gorman, P. A. & Pullin, D. I. 2005 Effect of Schmidt number on the velocity scalar cospectrum in isotropic turbulence with a mean scalar gradient. J. Fluid Mech. 532, 111–140.Google Scholar
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363–386.Google Scholar
Orszag, S. A. 1977 The statistical theory of turbulence. In Fluid Dynamics (ed. Balian, A. & Peube, J. L.), pp. 237–374. Gordon and Breach.Google Scholar
Overholt, M. R. & Pope, S. B. 1996 Direct numerical simulation of a passive scalar with imposed mean gradient in isotropic turbulence. Phys. Fluids 8 (11), 3128–3148.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Pouquet, A., Lesieur, M., Andre, J. C. & Basdevant, C. 1975 Evolution of high Reynolds number two-dimensional turbulence. J. Fluid Mech. 72, 305–319.Google Scholar
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 (6), 2118–2132.Google Scholar
Pumir, A. 1996 Turbulence in homogeneous shear flows. Phys. Fluids 8 (11), 3112–3127.Google Scholar
Rogers, M. M., Mansour, N. N. & Reynolds, W. C. 1989 An algebraic model for the turbulent flux of a passive scalar. J. Fluid Mech. 203, 77–101.Google Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Cambridge University Press.Google Scholar
Shen, X. & Warhaft, Z. 2000 The anisotropy of the small scale structure in high Reynolds number (r 𝜆 ∼ 1000) turbulent shear flow. Phys. Fluids 12 (11), 2976–2989.CrossRefGoogle Scholar
Shirani, E., Ferziger, J. H. & Reynolds, W. C.(1981) Mixing of a passive scalar in isotropic and sheared homogeneous turbulence. NASA Rep. No. Tf-15 NASA-CR-164938.Google Scholar
Sirivat, A. & Warhaft, Z. 1983 The effect of a passive cross-stream temperature gradient on the evolution of temperature variance and heat flux in grid turbulence. J. Fluid Mech. 128, 323–346.CrossRefGoogle Scholar
Speziale, C. G., Sarkar, S. & Gatski, T. B.(1990) Modeling the pressure–strain correlation of turbulence – an invariant dynamical systems approach. NASA Contractor Rep. 181979.Google Scholar
Sreenivasan, K. R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. Math. Phys. Sci. 434, 165–182.Google Scholar
Sreenivasan, K. R., Antonia, R. A. & Britz, D. 1979 Local isotropy and large structures in a heated turbulent jet. J. Fluid Mech. 94, 745–775.Google Scholar
Sreenivasan, K. R. & Tavoularis, S. 1980 On the skewness of the temperature derivative in turbulent flows. J. Fluid Mech. 101, 783–795.CrossRefGoogle Scholar
Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 311–347.Google Scholar
Venkataramani, K. S. & Chevray, R. 1978 Statistical features of heat transfer in grid-generated turbulence: constant-gradient case. J. Fluid Mech. 86, 513–543.Google Scholar
Waleffe, F. 1992 The nature of triad interactions in homogeneous turbulence. Phys. Fluids 4, 350–363.Google Scholar
Warhaft, Z. 1980 An experimental study of the effect of uniform strain on thermal fluctuations in grid-generated turbulence. J. Fluid Mech. 99, 545–573.Google Scholar
Watanabe, T. & Gotoh, T. 2007 Scalar flux spectrum in isotropic steady turbulence with a uniform mean gradient. Phys. Fluids 19.Google Scholar
Wyngaard, J. C. & Coté, O. R. 1972 Cospectral similarity in the atmospheric surface layer. Q. J. R. Meteorol. Soc. 98, 590–603.CrossRefGoogle Scholar