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Inertial-range intermittency and accuracy of direct numerical simulation for turbulence and passive scalar turbulence

Published online by Cambridge University Press:  15 October 2007

TAKESHI WATANABE  and
TOSHIYUKI GOTOH
TAKESHI WATANABE
Affiliation:
Graduate School of Engineering, Department of Engineering Physics, Nagoya Institute of Technology, Gokiso, Showa-ku, Nagoya, 466-8555, Japan CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
TOSHIYUKI GOTOH
Affiliation:
Graduate School of Engineering, Department of Engineering Physics, Nagoya Institute of Technology, Gokiso, Showa-ku, Nagoya, 466-8555, Japan CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
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Abstract

We examine the effects of the variation in dissipation-range resolution on the accuracy of inertial-range statistics and intermittency in terms of the direct numerical simulations of homogeneous turbulence and passive-scalar turbulence by changing the spatial resolution up to 20483 grid points while maintaining a constant Reynolds number at Rλ ≃ 180 or ≃ 420 and Schmidt number at Sc = 1. Although large fluctuations of the derivative fields depended strongly on Kmaxη and were underestimated when Kmaxη≃1, where Kmax is the maximum wavenumber in the computations and η is the mean Kolmogorov length, the behaviour of the spectra and the scaling exponents of the structure functions up to the eighth order in the range of scales greater than 10η was insensitive to variations in Kmaxη, even when Kmaxη≃1. The relationship between the spatial resolution and asymptotic tail of the probability density functions of the energy dissipation fields was studied using the multifractal model for dissipation, and the results were confirmed by comparison to the simulation data. Degradation of the statistics arises from modifications to the flow dynamics due to the finite wavenumber cutoff and the use of a coarser filter width for the data, which is obtained using a reasonable accuracy criterion for the flow dynamics. The effect of the former was less than that of the latter for the low-to-moderate-order statistics when Kmaxη≥1. We also discuss the universality of the inertial-range statistics with respect to variations in the dissipation-range characteristics.

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Papers
Information
Journal of Fluid Mechanics , Volume 590 , 10 November 2007 , pp. 117 - 146
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Batchelor, G. K., Howells, I. D. & Townsend, A. A. 1959 Small scale variation of convected quantities like temperature in a turbulent fluid. The case of large conductivity. J. Fluid Mech. 5, 134–139.CrossRefGoogle Scholar
Benzi, R., Biferale, L., Paladin, G., Vulpiani, A. & Vergassola, M. 1991 Multifractality in the statistics of the velocity gradients in turbulence. Phys. Rev. Lett. 67, 2299–2302.CrossRefGoogle ScholarPubMed
Bogucki, D., Domaradzki, J. A. & Yeung, P. K. 1997 Direct numerical simulations of passive scalars with Pr>1 advected by turbulent flow. J. Fluid Mech. 343, 111–130.CrossRefGoogle Scholar
Chen, S. & Cao, N. 1997 Anomalous scaling and structure instability in three-dimensional passive scalar turbulence. Phys. Rev. Lett. 78, 3459–3462.CrossRefGoogle Scholar
Chen, S., Doolen, G., Herring, J. R., Kraichnan, R. H., Orszag, S. A. & She, Z.-S. 1993 Far-dissipation range of turbulence. Phys. Rev. Lett. 70, 3051–3054.CrossRefGoogle ScholarPubMed
Corrsin, S. 1951 On the spectrum of isotropic temperature fluctuations in isotropic turbulence. J. Appl. Phys. 22, 469–473.CrossRefGoogle Scholar
Domaradzki, J. A. & Rogallo, R. S. 1990 Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence. Phys. Fluids A 2, 413–426.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence. Cambridge University Press.CrossRefGoogle 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.CrossRefGoogle Scholar
Goto, S. & Kida, S. 1999 Passive scalar spectrum in isotropic turbulence: prediction by the Lagrangian direct-interaction approximation. Phys. Fluids 11, 1936–1952.CrossRefGoogle Scholar
Gotoh, T., Nagaki, J. & Kaneda, Y. 2000 Passive scalar spectrum in the viscous-convective range in two-dimensional steady turbulence. Phys. Fluids 12, 155–168.CrossRefGoogle Scholar
Gotoh, T. & Watanabe, T. 2005 Statistics of transfer fluxes of the kinetic energy and scalar variance. J. Turbulence 6, No. 33 (18 pages).CrossRefGoogle Scholar
Ishihara, T., Kaneda, Y., Yokokawa, M., Itakura, K. & Uno, A. 2005 Energy spectrum in the near dissipation range of high resolution direct numerical simulation of turbulence. J. Phys. Soc. Japan 74, 1464–1471.CrossRefGoogle Scholar
Jimenez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.CrossRefGoogle Scholar
Kaneda, Y., Ishihara, T., Yokokawa, M., Itakura, K. & Uno, A. 2003 Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys. Fluids 15, L21–L24.CrossRefGoogle Scholar
Kerr, R. M. 1990 Velocity, scalar and transfer spectra in numerical turbulence. J. Fluid Mech. 211, 309–332.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. C. R. Acad. Sci. URSS 30, 301–305.Google Scholar
Kolmogorov, A. N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13, 82–85.CrossRefGoogle Scholar
Kraichnan, R. H. 1967 Intermittency in the very small scales of turbulence. Phys. Fluids 10, 2080–2082.CrossRefGoogle Scholar
Kraichnan, R. H. 1968 Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11, 945–953.CrossRefGoogle Scholar
Kraichnan, R. H. 1976 Eddy viscosity in two and three dimensions. J. Atmos. Sci. 3, 1521–1536.2.0.CO;2>CrossRefGoogle Scholar
Meneveau, C. & Sreenivasan, K. R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429–484.CrossRefGoogle Scholar
Moisy, F., Willaime, H., Andersen, J. S. & Tabeling, P. 2001 Passive scalar intermittency in low temperature helium flows. Phys. Rev. Lett. 86, 4827–4830.CrossRefGoogle ScholarPubMed
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics, Mechanics of Turbulence, Vol. 2, MIT Press.Google Scholar
Mydlarski, L. & Warhaft, Z. 1998 Passive scalar statistics in high-Péclet-number grid turbulence. J. Fluid Mech. 358, 135–175.CrossRefGoogle Scholar
Obukhov, A. M. 1949 Structure of the temperature field in turbulent flows. Isv. Geogr. Geophys. Ser. 13, 58–69.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Schumacher, J., Sreenivasan, K. R. & Yeung, P. K. 2005 Very fine structures in scalar mixing. J. Fluid Mech. 531, 113–122.CrossRefGoogle Scholar
Shraiman, B. I. & Siggia, E. D. 2000 Scalar turbulence. Nature 405, 639–646.CrossRefGoogle ScholarPubMed
Sreenivasan, K. R. 1995 On the universality of the Kolmogorov constant. Phys. Fluids 7, 2778–2784.CrossRefGoogle Scholar
Sreenivasan, K. R. 1996 The passive scalar spectrum and the Obukhov-Corrsin constant. Phys. Fluids 8, 189–196.CrossRefGoogle Scholar
Sreenivasan, K. R. 2004 Possible effects of small-scale intermittency in turbulent reacting flows. Flow Turb. Combust. 72, 115–141.CrossRefGoogle Scholar
Tsuji, Y. 2004 Intermittency effect on energy spectrum in high-Reynolds number turbulence. Phys. Fluids 16, L43–L46.CrossRefGoogle Scholar
Wang, L.-P., Chen, S. & Brasseur, J. G. 1999 Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 2. Passive scalar field. J. Fluid Mech. 400, 163–197.CrossRefGoogle Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203–240.CrossRefGoogle Scholar
Watanabe, T. & Gotoh, T. 2004 Statistics of a passive scalar in homogeneous turbulence. New J. Phys. 6, 40 (36 pages).CrossRefGoogle Scholar
Watanabe, T. & Gotoh, T. 2006 a Intermittency, field structure and accuracy of DNS in a passive scalar turbulence. In Proc. IUTAM Symp. on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamics (ed. S. Kida). Fluid Mechanics and Its Applications, vol. 79, pp. 171–176. Springer.CrossRefGoogle Scholar
Watanabe, T. & Gotoh, T. 2006 b Intermittency in passive scalar turbulence under the uniform mean scalar gradient. Phys. Fluids 18, 058105 (4 pages).CrossRefGoogle Scholar
Watanabe, T., Nakayama, Y. & Fujisaka, H. 2000 Large deviation statistics of the energy-flux fluctuation in the shell model of turbulence. Phys. Rev. E 61, R1024–R1027.Google ScholarPubMed
Wyngaard, J. C. 1968 Measurements of small-scale turbulence structure with hot wires. J. Sci. Instrum. 1, 1105–1108.CrossRefGoogle Scholar
Wyngaard, J. C. 1971 Spatial resolution of a resistance wire temperature sensor. Phys. Fluids 14, 2052–2054.CrossRefGoogle 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
Yakhot, V. & Sreenivasan, K. R. 2005 Anomalous Scaling of Structure Functions and Dynamics Constraints on Turbulence Simulations. J. Statist. Phys. 121, 823–841.CrossRefGoogle Scholar
Yeung, P. K., Donzis, D. A. & Sreenivasan, K. R. 2005 High-Reynolds-number simulation of turbulent mixing. Phys. Fluids 17, 081703 (4 pages).CrossRefGoogle Scholar
Yeung, P. K., Xu, S. & Sreenivasan, K. R. 2002 Schmidt number effects on turbulent transport with uniform mean scalar gradient. Phys. Fluids 14, 4178–4191.CrossRefGoogle Scholar