Articles

A closure model on velocity structure functions in homogeneous isotropic turbulence

Expand
  • 1. Laboratory of Mathematics and Physics, Ecole Centrale de Pékin, Beihang University, Beijing 100191, China;
    2. Co-Innovation Center for Advanced Aero-Engine, Beihang University, Beijing 100191, China;
    3. Faculty of Engineering and Physical Sciences, University of Surrey, Guildford GU2 7XH, U.K

Received date: 2016-10-22

  Revised date: 2017-05-12

  Online published: 2017-11-01

Supported by

Project supported by the National Natural Science Foundation of China (Nos. 11572025, 11202013, and 51420105008)

Abstract

Closure models started from Chou's work have been developed for more than 70 years, aiming at providing analytical tools to describe turbulent flows in the spectral space. In this study, a preliminary attempt is presented to introduce a closure model in the physical space, using the velocity structure functions as key parameters. The present closure model appears to qualitatively reproduce the asymptotic scaling behaviors at small and large scales, despite some inappropriate behaviors such as oscillations. Therefore, further improvements of the present model are expected to provide appropriate descriptions of turbulent flows in the physical space.

Cite this article

Le FANG, Feng GAO . A closure model on velocity structure functions in homogeneous isotropic turbulence[J]. Applied Mathematics and Mechanics, 2017 , 38(11) : 1627 -1634 . DOI: 10.1007/s10483-017-2274-9

References

[1] Chou, P. Y. On velocity correlations and the solution of equation of turbulent fluctuations. Quaterly Applied Mathematics, 3, 38-54(1945)
[2] Lesieur, M. Turbulence in Fluids, Kluwer Academic, Dordrecht (1997)
[3] Orszag, S. A. Lectures on the statistical theory of turbulence. Fluid Dynamics, Les Houches Summer School of Theoretical Physics (eds. Balian, R. and Peube, J. L.), Gorden and Breach, New York (1974)
[4] Bos, W. J. T. and Rubinstein, R. On the strength of the nonlinearity in isotropic turbulence. Journal of Fluid Mechanics, 733, 158-170(2013)
[5] Bos, W., Rubinstein, R., and Fang, L. Reduction of mean-square advection in turbulent passive scalar mixing. Physics of Fluids, 24(7), 075104(2012)
[6] Fang, L., Zhang, Y. J., Fang, J., and Zhu, Y. Relation of the fourth-order statistical invariants of velocity gradient tensor in isotropic turbulence. Physical Review E, 94(2), 023114(2016)
[7] Fang, L. Applying the Kolmogorov Equation to the Problem of Subgrid Modeling for Large-Eddy Simulation of Turbulence, Ph. D. dissertation, Ecole centrale de Lyon (2009)
[8] Tatarskii, V. I. Use of the 4/5 Kolmogorov equation for describing some characteristics of fully developed turbulence. Physics of Fluids, 17, 035110(2005)
[9] Fang, L., Bos, W. J. T., Zhou, X. Z., Shao, L., and Bertoglio, J. P. Corrections to the scaling of the second-order structure function in isotropic turbulence. Acta Mechanica Sinica, 26(2), 151-157(2010)
[10] Hill, R. J. and Boratav, O. N. Next-order structure-function equations. Physics of Fluids, 13, 276-283(2001)
[11] Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F., and Succi, S. Extended scalesimilarity in turbulent flows. Physical Review E, 48(1), R29-R32(1993)
[12] Benzi, R., Ciliberto, S., Baudet, C., and Chavarria, G. R. On the scaling of three-dimensional homogeneous and isotropic turbulence. Physica D, 80, 385-398(1995)
[13] McComb, W. D., Yoffe, S. R., Linkmann, M. F., and Berera, A. Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence. Physics of Fluids, 90, 053010(2014)
[14] Fang, L., Zhu, Y., Liu, Y. W., and Lu, L. P. Spectral non-equilibrium property in homogeneous isotropic turbulence and its implication in subgrid-scale modeling. Physics Letters A, 379(38), 2331-2336(2015)
[15] Chevillard, L., Meneveau, C., Biferale, L., and Toschi, F. Modeling the pressure Hessian and viscous Laplacian in turbulence:comparisons with direct numerical simulation and implications on velocity gradient dynamics. Physics of Fluids, 20, 101504(2008)
[16] Chevillard, L. and Meneveau, C. Lagrangian dynamics and statistical geometric structure of turbulence. Physics Review Letters, 97, 174501(2006)
[17] Wilczek, M. and Meneveau, C. Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields. Journal of Fluid Mechanics, 756, 191-225(2014)
[18] She, Z. S. and Leveque, E. Universal scaling law in fully developed turbulence. Physics Review Letters, 72, 336-339(1994)
[19] Bos, W. J. T., Chevillard, L., Scott, J., and Rubinstein, R. Reynolds number effects on the velocity increment skewness in isotropic turbulence. Physics of Fluids, 24, 015108(2012)
[20] Batchelor, G. K. The Theory of Homogeneous Turbulence, Cambridge University Press, Cambridge (1953)

Outlines

/

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals