Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-09T22:09:55.747Z Has data issue: false hasContentIssue false
  • English
  • Français

Dissipation, enstrophy and pressure statistics in turbulence simulations at high Reynolds numbers

Published online by Cambridge University Press:  08 February 2012

P. K. Yeung ,
D. A. Donzis  and
K. R. Sreenivasan
P. K. Yeung*
Affiliation:
Schools of Aerospace Engineering, Computational Science and Engineering, and Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
D. A. Donzis
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
K. R. Sreenivasan
Affiliation:
Courant Institute of Mathematical Sciences and Physics Department, New York University, New York, NY 10012, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We use data from well-resolved direct numerical simulations at Taylor-scale Reynolds numbers from 140 to 1000 to study the statistics of energy dissipation rate and enstrophy density (i.e. the square of local vorticity). Despite substantial variability in each of these variables, their extreme events not only scale in a similar manner but also progressively tend to occur spatially together as the Reynolds number increases. Though they possess non-Gaussian tails of enormous amplitudes, ratios of some characteristic properties can be closely linked to those of isotropic Gaussian random fields. We present results also on statistics of the pressure Laplacian and conditional mean pressure given both dissipation and enstrophy. At low Reynolds number intense negative pressure fluctuations are preferentially associated with rotation-dominated regions but at high Reynolds number both high dissipation and high enstrophy have similar effects.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Intermittency Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 700 , 10 June 2012 , pp. 5 - 15
Copyright
Copyright © Cambridge University Press 2012

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

1. Chen, S., Sreenivasan, K. R. & Nelkin, M. 1997 Inertial range scalings of dissipation and enstrophy in isotropic turbulence. Phys. Rev. Lett. 79, 1253–1256.CrossRefGoogle Scholar
2. Dimotakis, P. 2000 The mixing transition in turbulent flows. J. Fluid Mech. 409, 69–97.CrossRefGoogle Scholar
3. Donzis, D. A. & Yeung, P. K. 2010 Resolution effects and scaling in numerical simulations of passive scalar mixing in turbulence. Physica D 239, 1278–1287.CrossRefGoogle Scholar
4. Donzis, D. A., Yeung, P. K. & Sreenivasan, K. R. 2008 Dissipation and enstrophy in isotropic turbulence: scaling and resolution effects in direct numerical simulations. Phys. Fluids 20, 045108.CrossRefGoogle Scholar
5. Ishihara, T., Gotoh, T. & Kaneda, Y. 2009 Study of high-Reynolds number isotropic turbulence by direct numerical simulation. Annu. Rev. Fluid Mech. 41, 165–180.CrossRefGoogle Scholar
6. Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
7. 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
8. Kerr, R. M. 1985 Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58.CrossRefGoogle Scholar
9. Nelkin, M. 1999 Enstrophy and dissipation must have the same scaling exponents in the high Reynolds number limit of fluid turbulence. Phys. Fluids 11, 2202–2204.CrossRefGoogle Scholar
10. Pumir, A. 1994 A numerical study of pressure fluctuations in three-dimensional, incompressible, homogeneous, tropic turbulence. Phys. Fluids 6, 2071–2083.CrossRefGoogle Scholar
11. Sreenivasan, K. R. 1998 An update on the dissipation rate in homogeneous turbulence. Phys. Fluids 10, 528–529.CrossRefGoogle Scholar
12. Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472.CrossRefGoogle Scholar
13. Yakhot, V. 2008 Dissipation-scale fluctuations and mixing transition in turbulent flows. J. Fluid Mech. 606, 325–337.CrossRefGoogle Scholar
14. Yakhot, V. & Sreenivasan, K. R. 2005 Anomalous scaling of structure functions and dynamic constraints on turbulence simulations. J. Stat. Phys. 121, 823–841.CrossRefGoogle Scholar
15. Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.CrossRefGoogle Scholar