On the existence and scaling of structure functions in turbulence according to the data

TL;DR

This paper investigates the behavior of structure functions in turbulence, demonstrating divergence at high orders and providing a self-consistent correction to the Kolmogorov exponent based on data-matched velocity fields.

Contribution

It introduces a turbulence model with a self-consistent correction to the Kolmogorov exponent and analyzes the divergence of higher order structure functions.

Findings

The Kolmogorov exponent correction is zero in the model.

Higher order structure functions diverge beyond a certain order.

Results have implications for the statistical theory of homogeneous turbulence.

Abstract

We sample a velocity field that has an inertial spectrum and a skewness that matches experimental data. In particular, we compute a self-consistent correction to the Kolmogorov exponent and find that for our model it is zero. We find that the higher order structure functions diverge for orders larger than a certain threshold, as theorized in some recent work. The significance of the results for the statistical theory of homogeneous turbulence is reviewed.