The fractal geometry of interfaces and the multifractal distribution of dissipation in fully turbulent flows

We describe scalar interfaces in turbulent flowsvia elementary notions from fractal geometry. It is shown by measurement that these interfaces possess a fractal dimension of 2.35±0.05 in a variety of flows, and it is demonstrated that the uniqueness of this number is a consequence of the physical principle of Reynolds number similarity. Also, the spatial distribution of scalar and energy dissipation in physical space is shown to be multifractal. We compare thef() curves obtained from one- and two-dimensional cuts in several flows, and examine their value in describing features of turbulence in the three-dimensional physical space.