Kinematic orientation and dynamical redistribution of vorticity–strain alignment currents in turbulence

Abstract

The preferential alignment of vorticity with the intermediate eigenvector of the strain-rate tensor is a robust small-scale feature of turbulence, usually described through stationary alignment distributions. We ask an instantaneous question: in which direction, and how strongly, do vortex stretching and the vorticity-induced rotation of the strain eigenframe move vorticity between the three strain eigendirections? Writing these known restricted-Euler terms as pairwise currents between the squared alignment cosines, we measure them in direct numerical simulations of forced isotropic turbulence at Taylor-scale Reynolds numbers of 611 and 1300 and in turbulent channel flow. In preregistered analyses, replicated on unseen data, the three mean currents have fixed signs that orient the eigendirections in a closed loop. A variance-matched Gaussian reference reproduces this orientation but not the balance of the currents: its symmetry under reversal of the velocity gradient forces the currents into and out of the intermediate direction to cancel. In turbulence the restricted-Euler terms instead produce a clear net drift of alignment towards the intermediate direction, while the drift into the most extensional direction changes sign. The edge currents differ from the reference by factors of about 2.6, 0.43 and 0.23, with no detectable difference between the Reynolds numbers. The signs of the dominant currents persist under filtering up to 64 Kolmogorov lengths and in the outer channel region, where they attain the isotropic magnitude. The opposite net drift that the remaining terms must supply gives a quantitative target for models of the pressure Hessian and viscous effects. Preprint. Submitted to Open Transport (De Gruyter Brill), special collection Vortex Fluid Mechanics, 16 October 2026. Code, English versions of the analysis plans and all result files: https://github.com/SRT-Compute/alignment-edge-currents