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

Abstract

Whether turbulence intermittencies shall be described by a log-Poisson, a log-stable pdf or other distributions is still debated nowadays. In this paper, a bridge between polymer physics, self-avoiding walk and random vortex stretching is established which may help in getting a new insight on this topics. Actually a very simple relationship between stability index of the stable law and the well known Flory exponent stemming from polymer physics is established. Moreover the scaling of turbulence intermittencies with Reynolds number is also obtained and the overall picture is very close to Tennekes' simple model for the fine scale structure of turbulence [Phys. Fluids, 11, 3 (1968)] : vortex tubes of Kolmogorov length width are bend by bigger vortices of Taylor length scale. This thus results in both a simple and sound model with no fitting parameter needed.