Fractal dimension crossovers in turbulent passive scalar signals

The fractal dimension δg(1) of turbulent passive scalar signals is calculated from the fluid dynamical equation. δg(1) depends on the scale. For small Prandtl (or Schmidt) number Pr < 10-2 one gets two ranges, δg(1) = 1 for small-scale r and δg(1) = 5/3 for large r, both as expected. But for large Pr > 1 one gets a third, intermediate range in which the signal is extremely wrinkled and has δg(1) = 2. In that range the passive scalar structure function Dθ(r) has a plateau. We calculate the Pr-dependence of the crossovers. The plateau regime can be observed in a numerical solution of the fluid dynamical equation, employing a reduced wave vector set approximation introduced by us recently