Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-02-05T16:43:44.651Z Has data issue: false hasContentIssue false
  • English
  • Français

The dynamics of freely decaying two-dimensional turbulence

Published online by Cambridge University Press:  21 April 2006

M. E. Brachet ,
M. Meneguzzi ,
H. Politano  and
P. L. Sulem
M. E. Brachet
Affiliation:
CNRS, G.P.S., Ecole Normale Supérieure 24 rue Lhomond, 75231 Paris Cedex 05, France CNRS, Observatoire de Nice, B.P. 239, 06007 Nice Cedex, France
M. Meneguzzi
Affiliation:
CNRS, Service d'Astrophysique, C.E.N.-Saclay, 91191 Saclay, France
H. Politano
Affiliation:
CNRS, Observatoire de Nice, B.P. 239, 06007 Nice Cedex, France
P. L. Sulem
Affiliation:
School of Mathematical Sciences, Tel-Aviv University, 69978 Tel Aviv. Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulations of decaying high-Reynolds-number turbulence are presented at resolutions up to 8002 for general periodic flows and 20482 for periodic flows with large-scale symmetries. For turbulence initially excited at large scales, we characterize a transition of the inertial energy-spectrum exponent from n ≈ − 4 at early times to n ≈ − 3 when the turbulence becomes more mature. In physical space, the first regime is associated with isolated vorticity-gradient sheets, as predicted by Saffman (1971). The second regime, which is essentially statistical, corresponds to an enstrophy cascade (Kraichnan 1967; Batchelor 1969) and reflects the formation of layers resulting from the packing of vorticity-gradient sheets. In addition to these small-scale structures, the simulation displays vorticity macro-eddies which will survive long after the vorticity-gradient layers have been dissipated (McWilliams 1984). We validate the linear description of two-dimensional turbulence suggested by Weiss (1981), which predicts that coherent vortices will survive in regions where vorticity dominates strain, while vorticity-gradient sheets will be formed in regions where strain dominates. We show that this analysis remains valid even after vorticity-gradient sheets have been formed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 194 , September 1988 , pp. 333 - 349
Copyright
© 1988 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

Basdevant, C., Legras, B., Sadourny, R. & Béland, M. 1981 J. Atmos. Sci. 38, 2305.
Batchelor, G. K. 1959 J. Fluid Mech. 5 113.
Batchelor, G. K. 1969 Phys. Fluids 12, 233.
Benzi, R., Patarnello, S. & Santangelo, P. 1987 Europhys. Lett. 3, 811.
Brachet, M. E., Meiron, D. I., Orszag, S. A., Nickel, B. G., Morf, R. H. & Frisch, U. 1983 J. Fluid Mech. 130, 411.
Brachet, M. E., Meneguzzi, M., Politano, H. & Sulem, P. L. 1986 In Proc. European Turbulence Conference. Proceedings in Physics. Springer (in press).
Brachet, M. E., Meneguzzi, M. & Sulem, P. L. 1985 In Macroscopic Modeling of Turbulence Flow. Lecture Notes in Physics vol. 230, p. 344, Springer.
Brachet, M. E., Meneguzzi, M. & Sulem, P. L. 1986 Phys. Rev. Lett. 57, 683.
Brachet, M. E. & Sulem, P. L. 1984 In Proc. 9th Conf. on Numerical Methods in Fluid Mechanics. Lecture Notes in Physics vol. 218, p. 103, Springer.
Brachet, M. E. & Sulem, P. L. 1985 Prog. Astron. Aeron. 100, 100.
Deem, G. S. & Zabusky, N. J. 1971 Phys. Rev. Lett. 27, 396.
Fornberg, B. 1977 J. Comp. Phys. 25, 1.
Frisch, U., Pouquet, A., Sulem, P. L. & Meneguzzi, M. 1983 J. Méc. Théor. Appl. Numéro Spéciale, 2D. Turbulence, p. 191.
Frisch, U. & Sulem, P. L. 1984 Phys. Fluids 27, 1921.
Fyfe, D., Montgomery, D. & Joyce, G. 1977 Phys. Fluids 117, 369.
Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications. SIAM.
Herring, J. R. 1975 J. Atmos. Sci. 32, 2254.
Herring, J. R. & McWilliams, J. C. 1985 J. Fluid Mech. 153, 229.
Herring, J. R., Orszag, S. A., Kraichnan, R. H. & Fox, D. G. 1974 J. Fluid Mech. 66, 417.
Kida, S. 1981 Phys. Fluids 24, 604.
Kida, S. 1985 J. Phys. Soc. Japan 54, 2840.
Kida, S. & Yamada, M. 1984 In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi). Elsevier.
Kraichnan, R. H. 1967 Phys. Fluids 10, 1417.
Kraichnan, R. H. 1971 J. Fluid Mech. 47, 525.
Kraichnan, R. H. 1975 J. Fluid Mech. 67, 155.
Legras, B., Santangelo, P. & Benzi, R. 1988 High resolution numerical experiments for forced two-dimensional turbulence. Europhys. Lett., 5, 37.Google Scholar
Leith, C. 1968 Phys. Fluids 11, 671.
Lesieur, M. 1987 Turbulence in Fluids. Nijhoff.
Leslie, D. C. 1973 Developments in the Theory of Turbulence, Clarendon.
Lilly, D. K. 1969 Phys. Fluids Suppl. 12, 11, 240.
Lilly, D. K. 1971 J. Fluid Mech. 45, 395.
Lilly, D. K. 1972 Geophys. Fluid Dyn. 3, 289; 4, 1.
Mandelbrot, B. 1976 In Turbulence and Navier-Stokes equation. Lecture Notes in Mathematics vol. 565, p. 121. Springer.
McWilliams, J. C. 1984 J. Fluid Mech. 146, 21.
Orszag, S. A. 1977 In Proc. 5th Intl. Conf. on Numerical Methods in Fluids Dynamics Lecture Notes in Physics, vol. 59, p. 32.
Pouquet, A., Lesieur, M., André, J. C. & Basdevant, C. 1975 J. Fluid Mech. 72, 305.
Saffman, P. G. 1971 Stud. Appl. Maths 50, 377.
Sulem, C., Sulem, P. L. & Frisch, H. 1983 J. Comp. Phys. 50, 138.
Tatsumi, T. & Yanase, S. 1981 J. Fluid Mech. 110, 475.
Weiss, J. 1981 The dynamics of enstrophy transfer in two-dimensional hydrodynamics, LJI-TN-81-121. La Jolla Inst. La Jolla, California.