The spatial structure and statistical properties of homogeneous turbulence

TLDR

A direct numerical simulation at 240³ resolution produced a statistically stationary, homogeneous, isotropic turbulent field at Reλ≈150. The simulation revealed an inertial subrange in the energy spectrum, a velocity‑derivative distribution close to exponential yet non‑Gaussian, higher‑order moments and structure functions that deviate from intermittency predictions, and vorticity concentrated in elongated thin tubes a few dissipation scales wide and up to the integral scale long.

Abstract

A direct numerical simulation at resolution 240 3 is used to obtain a statistically stationary three-dimensional homogeneous and isotropic turbulent field at a Reynolds number around 1000 ( R λ ≈ 150). The energy spectrum displays an inertial subrange. The velocity derivative distribution, known to be strongly non-Gaussian, is found to be close to, but not, exponential. The n th-order moments of this distribution, as well as the velocity structure functions, do not scale with n as predicted by intermittency models. Visualization of the flow confirms the previous finding that the strongest vorticity is organized in very elongated thin tubes. The width of these tubes is of the order of a few dissipation scales, while their length can reach the integral scale of the flow.