Fractal geometry of isoscalar surfaces in turbulence: Theory and experiments

We present a Lagrangian calculation of the area of isothermal (or isoconcentration) surfaces in a medium of fluid turbulence. We argue that such surfaces appear fractal above some inner scale which depends on the Reynolds number. The fractal dimension is estimated theoretically. The theory is compared to experiments in which a dye is used as a passive scalar in various turbulent flows. We find excellent agreement in many details.