On geometrical properties of velocity derivatives in numerical turbulence

One of one most basic phenomena and distinctive features of three-dimensional turbulence is the predominant vortex stretching, which is manifested in positive net enstrophy generation σ ≡ ω i ω j s ij, <σ> > 0. This process consists both of vortex stretching (σ > 0) and of vortex compressing (σ < 0)¹ and cannot occur without its concomitants - vortex tilting and folding with large curvature of vortex lines. The ultimate clarification of relations between curvature and dynamically relevant quantities such as enstrophy ω 2, strain s 2 ≡ s ij s ij, enstrophy generation σ and it’s rate α ≡ σ/ω 2 can be obtained from looking at global properties. The hope is that some insights can be gained from local analysis. This what is mostly done in this work on the basis of a DNS data set of Navier-Stokes equations without forcing in a box with periodic boundary conditions and random Gaussian initial conditions. The results below correspond to the time moment right after the total enstrophy has reached its maximum at Re λ ≈ 75 [3].