Dimension of the carrier of turbulence: Intermittency in fluid mechanics

The multifractal model of turbulence assumes a concentration of the field of vorticity magnitude on a set of dimension smaller than 3. We examine the mechanism for the exponential growth of the vorticity magnitude, and estimate the fractal dimenison of its level sets on the basis of the equations of fluid mechanics. We propose a model of multifractal turbulence in which there is a connection between the fractal dimension of the level sets and the information dimension D1 of the carrier of the field of vorticity magnitude. Under the stated conditions we can estimate the dimension D1 and evaluate, within the framework of the multifractal model of turbulence, the values of the scaling exponents of velocity and temperature structure functions. We find exponents that are consistent with the available experimental information and which differ from the ones obtained by the Kolmogorov dimensional analysis.