J. Phys. I France
Volume 4, Numéro 8, August 1994
Page(s) 1115 - 1120
DOI: 10.1051/jp1:1994241
J. Phys. I France 4 (1994) 1115-1120

Short Communication

Free and layer turbulent percolation: topological instabilities and their suppression

A. Bershadskii1 and H. Branover2

1  P.O.Box 39953, Ramat-Aviv 61398, Tel-Aviv, Israel
2  Center for MHD-Studies, Ben-Gurion University, Beer-Sheva, Israel

(Received 25 April 1994, revised 26 May 1994, accepted 7 June 1994)

It is shown (theoretically and experimentally) that topological instabilities lead to free percolation of passive scalar in quasi two-dimensional turbulence that is characterized by the these-dimensional value of the critical exponent $\nu = 0.9$ and by spectral exponent " -4/3". Suppression of these instabilities transforms the percolation to layer-type process with $\nu = 4/3$ and spectral exponent "-7/3". In the last case fractal dimension of the passive scalar cluster equals 9/4 and fractal dimension of its perimeter equals 7/4 (i.e. is the same as fractal dimension of the hull of strictly two-dimensional percolation cluster). A good correspondence is found between the spectral and the fractal scaling laws and the atmospheric, numerical and laboratory experimental data.

© Les Editions de Physique 1994