Degrees of freedom of turbulence

We compute in the framework of a multifractal model for three-dimensional fully developed turbulence the number of degrees of freedom N as function of the Reynolds number R. $N— depends on the whole spectrum of singularities h related to the anomalous scaling of the velocity differences. On the other hand, we have also considered what is the total number $N_T^{\mathrm{*}}$ of equations needed in a computer simulation since N just has theoretical relevance. We stress, however, that the main features of intermittency can be described by an effective number N${̃}^{\mathrm{*}}$ which is much smaller than $N_T^{\mathrm{*}}$ because N${̃}^{\mathrm{*}}$ neglects very improbable events. We show that $N_T^{\mathrm{*}}$∝$R^3$ while we get from a fit of experimental data that N${̃}^{\mathrm{*}}$∝$R^{2.3}$ is of the same order of N∝$R^{2.2}$. .AE