Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-15T08:23:03.344Z Has data issue: false hasContentIssue false
  • English
  • Français

Point-source scalar turbulence

Published online by Cambridge University Press:  04 July 2007

ANTONIO CELANI,
MARCO MARTINS AFONSO and
ANDREA MAZZINO
ANTONIO CELANI
Affiliation:
CNRS, INLN, 1361 Route des Lucioles, 06560 Valbonne, France
MARCO MARTINS AFONSO
Affiliation:
Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot 76100, Israel
ANDREA MAZZINO
Affiliation:
Department of Physics – University of Genova & CNISM and INFN – Genova Section, via Dodecaneso 33, 16146 Genova, Italy
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

The statistics of a passive scalar randomly emitted from a point source is investigated analytically for the Kraichnan ensemble. Attention is focused on the two-point equal-time scalar correlation function, a statistical indicator widely used both in experiments and in numerical simulations. The only source of inhomogeneity/anisotropy is the injection mechanism, the advecting velocity being here statistically homogeneous and isotropic. The main question we address is on the possible existence of an inertial range of scales and a consequent scaling behaviour. The question arises from the observation that for a point source the injection scale is formally zero and the standard cascade mechanism cannot thus be taken for granted. We find from first principles that an intrinsic integral scale, whose value depends on the distance from the source, emerges as a result of sweeping effects. For separations smaller than this integral scale a standard forward cascade occurs. This is characterized by a Kolmogorov–Obukhov power-law behaviour as in the homogeneous case, except that the dissipation rate is also dependent on the distance from the source. Finally, we also find that the combined effect of a finite inertial-range extent and of inhomogeneities causes the emergence of subleading anisotropic corrections to the leading isotropic term, that are here quantified and discussed.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007, pp. 189 - 198
Copyright
Copyright © Cambridge University Press 2007

References

REFERENCES

Basu, S., Foufoula-Georgiou, E. & Porté-Agel, F. 2004 Synthetic turbulence, fractal interpolation and large-eddy simulation. Phys. Rev. E 70, 026310.Google ScholarPubMed
Biferale, L. & Procaccia, I. 2005 Anisotropy in turbulent flows and in turbulent transport. Phys. Rep. 414, 43–164.CrossRefGoogle Scholar
Celani, A., MartinsAfonso, M. Afonso, M. & Mazzino, A. 2005 Coarse-grained scalar transport: closures and large-eddy simulations. In Progress in Turbulence 2, Proc. iTi Conf. on Turbulence, Bad Zwischenahn (Germany), September 25–28, 2005 (ed. Oberlack, M., Guenther, S., Weller, T., Khujadze, G., Osman, A., Frewer, M. & Peinke, J.). Springer (in press).Google Scholar
Celani, A., MartinsAfonso, M. Afonso, M. & Mazzino, A. 2006 Coarse-grained description of a passive scalar. J. Turb. 7 (52), 1–18.CrossRefGoogle Scholar
Celani, A. & Seminara, A. 2005 Large-scale structure of passive scalar turbulence. Phys. Rev. Lett. 94, 214503.CrossRefGoogle ScholarPubMed
Celani, A. & Seminara, A. 2006 Large-scale anisotropy in scalar turbulence. Phys. Rev. Lett. 96, 184501.CrossRefGoogle ScholarPubMed
Donsker, M. D. 1964 On function space integrals. In Proc. Conf. on the Theory and Applications of Analysis in Function Space, Dedham (MA), June 9–13, 1963 (ed. Martin, W. T. & Segal, I.), ch. 2, pp. 17–30. MIT Press.Google Scholar
Falkovich, G. & Fouxon, A. 2005 Anomalous scaling of a passive scalar in turbulence and in equilibrium. Phys. Rev. Lett. 94, 214502.CrossRefGoogle ScholarPubMed
Falkovich, G., Gawcedzki, K. & Vergassola, M. 2001 Particles and fields in fluid turbulence. Rev. Mod. Phys. 73, 913–975.CrossRefGoogle Scholar
Furutsu, K. 1963 On the statistical theory of electromagnetic waves in a fluctuating medium. J. Res. Natl Bur. Standards D 67, 303–323.Google 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. 1994 Anomalous scaling of a randomly advected passive scalar. Phys. Rev. Lett. 72, 1016–1019.CrossRefGoogle ScholarPubMed
Martins Afonso, M., Celani, A., Festa, R. & Mazzino, A. 2003 Large-eddy-simulation closures of passive scalar turbulence: a systematic approach. J. Fluid Mech. 496, 355–364.CrossRefGoogle Scholar
Martins fonsoA, M. A, M., Celani, A. & Mazzino, A. 2004 Closures for large-eddy simulations of passive scalars. In Advances in Turbulence X, Proceedings of the Tenth European Turbulence Conference, Trondheim (Norway), June 29–July 2, 2004 (ed. Andersson, H. I. & Krogstad, P. A.), pp. 319–322. CIMNE.Google Scholar
Martins fonso, A M., & Sbragaglia, M. 2005 Inhomogeneous anisotropic passive scalars. J. Turb. 6 (10), 1–13.Google Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.CrossRefGoogle Scholar
Novikov, E. A. 1965 Functionals and the random-force method in turbulence theory. Sov. Phys. JETP 20, 1290–1294.Google Scholar
Scotti, A. & Meneveau, C. 1997 Fractal model for coarse-grained partial differential equations. Phys. Rev. Lett. 78, 867–870.CrossRefGoogle Scholar
Toschi, F., Amati, G., Succi, S., Benzi, R. & Piva, R. 1999 Intermittency and structure functions in channel flow turbulence. Phys. Rev. Lett. 82, 5044–5047.CrossRefGoogle Scholar