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 pressure-Hessian—which are analysed here using direct numerical simulations of isotropic turbulence on up to grid points, and Taylor-scale Reynolds numbers in the range 140–1300. We extract the statistics involved in amplification of strain and condition them on the magnitude of strain. We find that strain is self-amplified by the quadratic nonlinearity, and depleted via vortex stretching, whereas pressure-Hessian acts to redistribute strain fluctuations towards the mean-field and hence depletes intense strain. Analysing 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. By contrast, the self-amplification acts to deplete the other two eigenvalues, whereas vortex stretching acts to amplify them, with both effects cancelling 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 tube-like regions of intense vorticity due to fundamental differences in their amplifying mechanisms.This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’.

Highlights

  • The dissipation rate of kinetic energy, defined as= 2νSijSij, where Sij = ∂ ui ∂ xj + ∂ uj ∂ xi (1.1)plays an indispensable role in our understanding of turbulent fluid flows

  • 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 and pressure-Hessian—which are analysed here using direct numerical simulations of isotropic turbulence on up to 12 2883 grid points, and Taylor-scale Reynolds numbers in the range 140–1300

  • We have investigated the three nonlinear processes involved in the transport equation for Σ (see equation (3.2)), viz., the strain self-amplification, vortex stretching and strain-pressure Hessian correlation, by analysing their statistics conditioned on Σ

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Summary

Generation of intense dissipation in high Reynolds number turbulence

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 pressure-Hessian—which are analysed here using direct numerical simulations of isotropic turbulence on up to 12 2883 grid points, and Taylor-scale Reynolds numbers in the range 140–1300. We find that strain is selfamplified by the quadratic nonlinearity, and depleted via vortex stretching, whereas pressure-Hessian acts to redistribute strain fluctuations towards the meanfield and depletes intense strain. The self-amplification acts to deplete the other two eigenvalues, whereas vortex stretching acts to amplify them, with both effects cancelling 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. This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’

Introduction
DΣ Dt
Findings
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