Extreme dissipation and intermittency in turbulence at very high Reynolds numbers

TL;DR

This paper introduces a new model for predicting extreme dissipation events in turbulence at very high Reynolds numbers, emphasizing the role of shear layers and their layered substructures.

Contribution

A novel dissipation PDF model based on significant shear layers with layered substructures, providing Reynolds number scalings consistent with data.

Findings

Model predicts dissipation maxima and variance scaling with Reynolds number.

Power law scaling exponent increases with Reynolds number.

Implications for turbulence at atmospheric and astrophysical scales.

Abstract

Extreme dissipation events in turbulent flows are rare, but they can be orders of magnitude stronger than the mean dissipation rate. Despite its importance in many small-scale physical processes, there is presently no accurate theory or model for predicting the extrema as a function of the Reynolds number. Here, we introduce a new model for the dissipation PDF based on the concept of significant shear layers, which are thin regions of elevated local mean dissipation. At very high Reynolds numbers these significant shear layers develop layered substructures. The flow domain is divided into the different layer regions and a background region, each with their own PDF of dissipation. The volume weighted regional PDFs are combined to obtain the overall PDF, which is subsequently used to determine the dissipation variance and maximum. The model yields Reynolds number scalings for the dissipation maximum and variance, which are in agreement with the available data. Moreover, the power law scaling exponent is found to increase gradually with the Reynolds number, which is also consistent with the data. The increasing exponent is shown to have profound implications for turbulence at atmospheric and astrophysical Reynolds numbers. The present results strongly suggest that intermittent significant shear layer structures are key to understanding and quantifying the dissipation extremes, and, more generally, extreme velocity gradients.