Statistics of Small-Scale Structure of Homogeneous Isotropic Turbulence

Abstract

In order to study the properties of the inertial subrange, we have recently generated a data-base by direct numerical simulation (DNS) with 5123 grid points of forced homogeneous isotropic turbulence obeying the incompressible Navier-Stokes (NS) equations. In the DNS, the enstrophy grows monotonically in time and then attains its peak value at about t = 12.0 (in eddy turnover time units), after which the turbulence is in a quasi-steady state. The Taylor scale Reynolds number R λ at t = 12 is 126, and the energy spectrum E(k) is close to K 0 ∈2/3 K −5/3, (K 0 = 2.28) in the wavenumber range 8 < k < 18. Here we study the small-scale structure of turbulence on the basis of the data-base. Jimenez et al. [1] analyzed the structure of intense vorticity by using a data-base with 5123 grid points of a homogeneous isotropic turbulent field of R λ = 169. We analyze our data-base by paying attention mainly to the structure at length scales in the inertial subrange. First, we investigate the probability distribution functions (pdf’s) of the Eulerian and Lagrangian time-derivative fields and fourthorder velocity moments, to study the intermittent and non-Gaussian nature of turbulence. Next, in order to get some idea on the mechanism by which the turbulence exhibits the intermittent and non-Gaussian nature, we analyze the turbulent field from the viewpoint of vortex dynamics by visualizing the regions with high vorticity magnitude, high dissipation, and high enstrophy generation, as well as the regions where the vorticity and the eigenvector of rate-of-strain tensor align well. Finally, in order to study the flow structures at the scales of the inertial subrange, we analyze geometric relations between the vorticity and rate-of-strain tensor at several coarse-grained levels.