Generation of intense dissipation in high Reynolds number turbulence

TL;DR

This study investigates the mechanisms behind intense energy dissipation fluctuations in high Reynolds number turbulence, revealing the roles of strain amplification, vortex stretching, and pressure Hessian through advanced simulations.

Contribution

It provides a detailed analysis of strain amplification mechanisms and their eigenvalue dynamics in turbulence at unprecedented Reynolds numbers using direct numerical simulations.

Findings

Strain is self-amplified by quadratic nonlinearity.

Vortex stretching depletes strain fluctuations.

Pressure Hessian redistributes strain towards the mean, reducing intense strain.

Abstract

Intense fluctuations of energy dissipation rate in turbulent flows result from the self-amplification of strain rate via a quadratic nonlinearity, with contributions from vorticity (via the vortex stretching mechanism) and the pressure Hessian tensor, which we analyze here using direct numerical simulations of isotropic turbulence in periodic domains of up to $12288^3$ grid points, and Taylor-scale Reynolds numbers in the range $140-1300$. We extract the statistics of various terms involved in amplification of strain and additionally condition them on the magnitude of strain. We find that strain is overall self-amplified by the quadratic nonlinearity, and depleted via vortex stretching; whereas pressure Hessian acts to redistribute strain fluctuations towards the mean-field and thus depleting intense strain. Analyzing the intense fluctuations of strain in terms of its eigenvalues reveals that the net amplification is solely produced by the third eigenvalue, resulting in strong compressive action. In contrast, the self-amplification terms acts to deplete the other two eigenvalues, whereas vortex stretching acts to amplify them, both effects canceling each other almost perfectly. The effect of the pressure Hessian for each eigenvalue is qualitatively similar to that of vortex stretching, but significantly weaker in magnitude. Our results conform with the familiar notion that intense strain is organized in sheet-like structures, which are in the vicinity of, but never overlap with regions of intense vorticity due to fundamental differences in their amplifying mechanisms.