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

TL;DR

This paper introduces a simple, parameter-free model linking turbulence intermittencies to concepts from polymer physics and vortex dynamics, providing new insights into their statistical behavior and scaling with Reynolds number.

Contribution

It establishes a novel relationship between the stability index of turbulence distributions and the Flory exponent from polymer physics, connecting vortex stretching with intermittency statistics.

Findings

Derived a relationship between stable law index and Flory exponent.

Predicted turbulence intermittency scaling with Reynolds number.

Aligned the model with Tennekes' vortex tube concept.

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.