Non-Kolmogorov scaling exponents and the geometry of high Reynolds number turbulence

Scaling behavior in turbulence is studied on the basis of its relation to the wrinkling, or fractalization, of the graph of the velocity field in 3+3 dimensions. We propose a novel mechanism for deviations from the Kolmogorov exponents, which is realized if the fine structure of turbulence tends locally towards two dimensionality. It is argued that some of the popular fractal and multifractal models of intermittency in turbulence are not consistent with fluid mechanics, and miss some essential physics.