Abstract
Corrections of Batchelor's spectral law “−1” of passive scalar-fluctuations are obtained by taking into account the topological instabilities of small-scale vortex sheets: “−4/3” for supercritical and “−5/4” for subcritical regimes. The corresponding fractal dimensions of the scalar interface areD σ=8/3 for supercritical andD σ=11/4 for subcritical regimes. Good agreement with experimental data is established.
This is a preview of subscription content, log in via an institution to check access.
References
G. K. Batchelor, Small-scale variation of convected quantities like temperature in turbulent fluid.J. Fluid Mech. 5:113–133 (1959).
A. S. Monin and A. M. Yaglom,Statistical Fluid Mechanics, Vol. 2 (MIT Press, Cambridge, 1975).
K. R. Sreenivasan and R. R. Prasad, New results on the fractal and multifractal structure of the large Schmidt number passive scalars in fully developed turbulent flows,Physica D 38:322–329 (1989).
R. R. Prasad and K. R. Sreenivasan, The measurement and interpretation of fractal dimensions of the scalar interface in turbulent flows,Phys. Fluids A 2(5):792–807 (1990).
K. R. Sreenivasan, Fractals and multifractals in fluid turbulence,Annu. Rev. Fluid Mech. 23:539–600 (1991).
A. A. Townsend, On the fine-scale structure of turbulenceProc. R. Soc. Lond. A 208:534–542 (1951).
A. A. Townsend. The diffusion of heat spots in isotropic turbulence,Proc. R. Soc. Lond. A 209:418–430 (1951).
H. K. Moffatt, Transport effects associated with turbulence, with particular attention to the influence of helicity,Rep. Prog. Phys. 46:621–664 (1983).
A. Bershadskii and A. Tsinober, Local anisotropic effects on multifractality of turbulence.Phys. Rev. E 48:282–287 (1993).
A. Bershadskii, E. Kit, and A. Tsinober, Spontaneous breaking of reflexional symmetry in real quasi-two-dimensional turbulence: stochastic travelling waves and helical solitons in atmosphere and laboratory.Proc. R. Soc. Lond. A 441:147–155 (1993).
J. C. Vassilicos, On the geometry of lines in two-dimensional turbulence, inAdvances in Turbulence 2, H. H. Fernholtz and H. E. Fieldler,eds. Springer-Verlag, Berlin, 1989), pp. 404–411.
J. C. Vassilicos and J. C. R. Hunt, Fractal dimensions and spectra of interfaces with applications to turbulence,Proc. R. Soc. Lond. A 435:505–534 (1991).
G. D. Nastrom, W. H. Jasperson, and K. S. Gage, Horizontal spectra of atmospheric traces measured during the global atmospheric sampling program,J. Geophys. Res. D 91:13201–13209 (1986).
S. Lovejoy, The area-perimeter relationship for rain and cloud area.Science 216:185–187 (1982).
H. L. Grantet al., The spectrum of temperature fluctuations in turbulent flows,J. Fluid Mech. 34:423–442 (1968).
R. J. Hill, Comparison of experiment with a new theory of the turbulent temperature structure functions,Phys. Fluids A 3:1572–1576 (1991).
Author information
Authors and Affiliations
Additional information
Communicated by J. L. Lebowitz
Rights and permissions
About this article
Cite this article
Bershadskii, A. Topological and fractal properties of turbulent passive scalar fluctuations at small scales. J Stat Phys 77, 909–914 (1994). https://doi.org/10.1007/BF02179468
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02179468