Refined scaling hypothesis for breakdown coefficients in turbulence

We study the statistics of Novikov’s breakdown coefficients, which represent ratios between energy dissipation rates at different length scales in turbulence. The distribution of their logarithms is shown to be very closely reproduced by an analytic function that we obtain from a hierarchical stochastic process for the turbulent cascade. Correlations and deviation from Gaussianity in the model are accounted for by two parameters, one of which can be interpreted as a generalized dimension. Finally, we illustrate the lack of power-law scaling in the moments of the breakdown coefficients and propose an analytical approximation scheme for them.