Abstract
Simple lattice vortex models are presented that exhibit vortex percolation along lines in a temperature/chemical potential plane. Parts of these lines can be identified with the percolation threshold at the inertial range of turbulence, and other parts are analogous to the transition in a three-dimensionalXY model that may model the λ. transition in superfluidity. Flory exponents at percolation are calculated; for nonnegative temperatures, their values approximate the standard Flory value, and are approximately constant along the transition lines, in agreement with recent conjectures. Conclusions regarding coherent structures in turbulence are also reached.
Similar content being viewed by others
References
A. J. Chorin,Commun. Math. Phys. 141:619 (1991).
S. R. Shenoy,Phys. Rev. B 40:5056 (1989).
G. Williams,Phys. Rev. Lett. 59:1926 (1987).
L. Onsager,Nuovo Cimento (Suppl.) 6:279 (1949).
P. G. de Germes,Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, New York, 1971).
A. J. Chorin,Lectures on Turbulence Theory (Publish/Perish, Boston, 1975).
A. J. Chorin,Commun. Math. Phys. 114:167 (1988).
A. J. Chorin and J. Akao,Physica D 52:403 (1991).
A. G. Bershadski,Sov. Phys. Usp. 33:1073 (1990).
J. Kosterlitz and D. J. Thouless,J. Phys. C: Solid State Phys. 6:1181–1203 (1973).
J. Fröhlich and T. Spencer,Commun. Math. Phys. 81:527 (1981).
G. Grimmett,Percolation (Springer, New York, 1989).
A. J. Chorin,Commun. Pure Appl. Math. 39 (special issue): S47 (1986).
P. Bernard and J. Thomas, Vortex dynamics in near-wall turbulence, University of Maryland report (1991).
M. Head and P. Bandyopadhyay,J. Fluid Mech. 107:297 (1981).
D. Stauffer,Introduction to Percolation Theory (Taylor and Francis, London, 1985).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chorin, A.J. A vortex model with superfluid and turbulent percolation. J Stat Phys 69, 67–78 (1992). https://doi.org/10.1007/BF01053783
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01053783