Local energy flux of turbulent flows

We investigate the local energy flux rate Pi(l) (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, skewness, and kurtosis of these fluctuations are shown to increase as the filtering scale is decreased. Furthermore, we calculate the joint PDF of Pi(l) (x) with the local filtered strain rate S-l and the enstrophy Omega(l). 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(l)>(S) proportional to l(2)S(l)(3) in support of 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 modeling directions.