Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-09T21:38:52.120Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of intense vorticity in isotropic turbulence

Published online by Cambridge University Press:  26 April 2006

Javier Jiménez ,
Alan A. Wray ,
Philip G. Saffman  and
Robert S. Rogallo
Javier Jiménez
Affiliation:
Centre for Turbulence Research, Stanford University, Stanford, CA 94305, USA Permanent address: School of Aeronautics, Pl. Cardenal Cisneros 3, 28040 Madrid, Spain.
Alan A. Wray
Affiliation:
NASA Ames Research Centre, Moffett Field, CA 94035, USA
Philip G. Saffman
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena, CA 91125, USA
Robert S. Rogallo
Affiliation:
NASA Ames Research Centre, Moffett Field, CA 94035, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The structure of the intense-vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers, in the range Reλ = 35–170. In accordance with previous investigators this vorticity is found to be organized in coherent, cylindrical or ribbon-like, vortices (‘worms’). A statistical study suggests that they are simply especially intense features of the background, O(ω′), vorticity. Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow. An interesting observation is that the Reynolds number γ/ν, based on the circulation of the intense vortices, increases monotonically with Reλ, raising the question of the stability of the structures in the limit of Reλ → ∞. Conversely, the average rate of stretching of these vortices increases only slowly with their peak vorticity, suggesting that self-stretching is not important in their evolution. One- and two-dimensional statistics of vorticity and strain are presented; they are non-Gaussian and the behaviour of their tails depends strongly on the Reynolds number. There is no evidence of convergence to a limiting distribution in this range of Reλ, even though the energy spectra and the energy dissipation rate show good asymptotic properties in the higher-Reynolds-number cases. Evidence is presented to show that worms are natural features of the flow and that they do not depend on the particular forcing scheme.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 255 , October 1993 , pp. 65 - 90
Copyright
© 1993 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

Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain in simulated Navier Stokes turbulence. Phys. Fluids 30, 3243–3253.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. & Townsend, A. A. 1949 The nature of turbulent motion at large wave numbers. Proc. R. Soc. Lond A 199, 238–255.Google Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1987 Spectral Methods in Fluid Dynamics, pp. 85–86, Springer.
Castaing, B., Gagne, Y. & Hopfinger, E. J. 1990 Velocity probability density functions of high Reynolds number turbulence. Physica D 46, 177–200.Google Scholar
Champagne, F. H. 1978 The fine-scale structure of the turbulent velocity field. J. Fluid Mech. 86, 67–108.Google Scholar
Compte-Bellot, G. & Corrsin, S. 1971 Simple Eulerian time correlations of full and narrow-band velocity signals in grid-generated isotropic turbulence. J. Fluid Mech. 48, 273–337.Google Scholar
Domaradzki, J. A. 1992 Nonlocal triad interactions and the dissipation range of isotropic turbulence. Phys. Fluids A 4, 2037–2045.Google Scholar
Douady, S., Couder, Y. & Brachet, M. E. 1991 Direct observation of the intermittency of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983–986.Google Scholar
Hosokawa, I. & Yamamoto, K. 1990 Intermittency of dissipation in directly simulated fully developed turbulence. J. Phys. Soc. Japan 59, 401–404.Google Scholar
Jiménez, J. 1991 On small scale vortices in turbulent flows. CTR Ann. Res. Briefs, pp. 45–56 (see also Phys. Fluids A 4, 652–654.)Google Scholar
Kerr, R. M. 1985 Higher order derivative correlation and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluids a very large Reynolds numbers. Dokl. Nauk. SSSR. 30, 301–305.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Moffatt, H. K. 1989 Fixed points of turbulent dynamical systems and suppression of nonlinearity. In Whither Turbulence? Turbulence at the Crossroads (ed. J. L. Lumley) Lecture Notes in Physics, vol. 357, pp. 250–257. Springer.
Ruetsch, G. R. & Maxey, M. R. 1991 Small scale features of vorticity and passive scalar fields in homogeneous isotropic turbulence. Phys. Fluids A 3, 1587–1597.Google Scholar
She, Z.-S. 1991 Intermittency and non-gaussian statistics in turbulence. Fluid Dyn. Res. 8, 143–159.Google Scholar
She, Z.-S., Jackson, E. & Orszag, S. A. 1990 Structure and dynamics of homogeneous turbulence, models and simulations. Proc. R. Soc. Lond. A 434, 101–124.Google Scholar
Siggia, E. D. 1981 Numerical study of small scale intermittency in three dimensional turbulence. J. Fluid Mech. 107, 375–406.Google Scholar
Sreenivasan, K. R. 1984 On the scaling of the turbulence energy dissipation rate. Phys. Fluids 27, 1048–1051.Google Scholar
Townsend, A. A. 1951 On the fine scale structure of turbulence. Proc. R. Soc. Lond. A 208, 534–542.Google Scholar
Van Atta, C. W. & Antonia, R. A. 1980 Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives. Phys. Fluids 23, 252–257.Google Scholar
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1–25.Google Scholar
Wei, T. & Willmarth, W. W. 1989 Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204, 57–95.Google Scholar