Topological and fractal properties of turbulent passive scalar fluctuations at small scales

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=8/3 for supercritical andD=11/4 for subcritical regimes. Good agreement with experimental data is established.