Simple model for turbulence intermittencies based on self-avoiding random vortex stretching

Whether statistics of intermittencies (between small and large eddies) in homogeneous and isotropic turbulence should be described by a logarithmic-Poisson, a logarithmic-stable probability density function, or other is still debated nowadays. In this paper, a bridge between polymer physics, self-avoiding walk, and random vortex stretching is established which may help to obtain new insights on this topic. A very simple relationship between the stability index of the Lévy stable law and Flory's exponent stemming from statistics of linear polymer growth is established. Moreover, the scaling of turbulence intermittencies with Reynolds number is also explained and the overall picture is given of smallest vortex tubes of Kolmogorov length width (i.e., the smallest dissipative eddies) bent by bigger vortices of Taylor length scale (i.e., the mean dissipative eddies), themselves stretched by the bigger eddies in a continuous cascade. This results in both a simple and sound model with no fitting parameters required.