Free and layer turbulent percolation: topological instabilities and their suppression

Abstract

It is shown (theoretically and experimentally) that topological instabilities lead to free percolation of passive scalar in quasi two-dimensional turbulence that is characterised by the three-dimensional value of the critical exponent ν=0.9 and by spectral exponent «-4/3». Suppression of these instabilities transforms the percolation to layer-type process with ν=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