Scaling exponents for active scalars

Journal of Statistical Physics

Volumn 90, Issue 3-4, 1998, Pages 571-595

  Constantin, Peter ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

3D active scalars; Dirichlet quotients; Navier Stokes equations

Indexed keywords

EID: 0031999043     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023264617618     Document Type: Article

References (15)

1. A. N. Kolmogorov, Local structure of turbulence in an incompressible fluid at very high Reynolds number, Dokl. Akad. Nauk. SSSR 30:299 (1941).
2. U. Frisch, Turbulence, Cambridge University Press.
3. R. H. Kraichnan, Small-scale structure of a scalar field converted by turbulence, Phys. of Fluids, 11(5):945-953 (1968).
4. R. H. Kraichnan, Anomalous scaling of a randomly advected passive scalar, Phys. Rev. Lett. 72(7):1016-1019 (1994).
5. P. Constantin, Regularity results for incompressible fluids, in The Earth's climate as a dynamical system, ANL/MCS-TM-170, pp. 21-38 (1992).
6. P. Constantin, Geometric statistics in turbulence, SIAM Rev. 36:73-98 (1994).
7. P. Constantin, A. Majda, and E. Tabak, Formation of strong fronts in the 2D quasi-geostrophic thermal active scalar, Nonlinearity 7:1495-1533 (1994).
8. M. Chertkov, G. Falkovich, L. Kolokolov, and V. Lebedev, Statistics of a passive scalar adverted by a large scale two-dimensional velocity field: analytic solution, Phys. Rev. E 51(6):5609-5627 (1995).
9. G. Eyink and J. Xin, Universality of the inertial-convective range in Kraichnan's model of a passive scalar, preprint (July 4, 1996).
10. K. Gawedzki and A. Kupiainen, Anomalous scaling of the passive scalar, Phys. Rev. Lett. 75-21 (1995), 3834-3837.
11. R. H. Kraichnan, V. Yakhot, and S. Chen, Scaling relations for a randomly advected passive scalar field, Phys. Rev. Lett. 75(2):240-243 (1995).
12. V. L'vov, I. Procaccia, and A. Fairhall, Anomalous scaling in fluid mechanics: the case of the passive scalar, Phys. Rev. E 50(6):4684-4704 (1994).
13. B. Shraiman and E. Siggia, Anomalous scaling of a passive scalar in turbulent flow, C.R. Acad. Sci. Paris 321(IIb): 279-284 (1995).
14. E. M. Stein, Singular integrals and differentiability properties of functions (Princeton University Press, Princeton 1970).
15. P. Constantin and Ch. Fefferman, Scaling exponents in fluid turbulence: some analytic results, Nonlinearity 7:41-57 (1994).