On the local energy flux of turbulent flows

Abstract

We investigate the local energy flux rate ${\Pi }_{\ell }(\mathbf{x})$ towards small scales in isotropic turbulent flows using direct numerical simulations and applying different low-pass filters. Two different filters are examined, a sharp Fourier filter and a Gaussian filter. The probability density function (pdf) of the local energy flux is calculated for the different filters and for different filtering scales. It is shown that the local energy flux is a largely fluctuating quantity taking both negative and positive values and this is more pronounced for the sharp filter. The variance, the skewness and the kurtosis of these fluctuations are shown to increase as the filtering scale is decreased. Furthermore we calculate the joint pdf of ${\Pi }_{\ell }(\mathbf{x})$ with the local filtered strain rate $S_{\ell }$ and the enstrophy ${\Omega }_{\ell }$. The flux shows a good correlation with the strain but not with the enstrophy. It is shown that its conditional mean value scales like $<{\Pi }_{\ell }{>}_S\propto {\ell }^2{S}_{\ell }^3$ in support to the Smagorinsky eddy viscosity model. Nonetheless strong fluctuations exist around this value that also need to be modeled. We discuss the implications of our results for subgrid scale models, and propose new modelling directions.

References in corpus (13)

• Dynamical ensembles in stationary states
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Cascades and transitions in turbulent flows
• The Joint Cascade of Energy and Helicity in Three-Dimensional Turbulence
• Localness of energy cascade in hydrodynamic turbulence, I. Smooth coarse-graining
• Localness of energy cascade in hydrodynamic turbulence, II. Sharp spectral filter
• Modeling the pressure Hessian and viscous Laplacian in Turbulence: comparisons with DNS and implications on velocity gradient dynamics
• Fluctuations of energy flux in wave turbulence
• Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence
• Is the Kelvin Theorem Valid for High-Reynolds-Number Turbulence?
• Lagrangian time correlations of vorticity alignments in isotropic turbulence: observations and model predictions
• Fluctuations of entropy production in turbulent thermal convection
• On the probability distribution of power fluctuations in turbulence

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