Abstract

Co-Author: Yoshifumi Kimura (Graduate School of Mathematics, Nagoya University) It is known that, in incompressible homogeneous and isotropic Navier-Stokes turbulence, the vorticity vector tends to align with the eigenvector corresponding to the intermediate eigenvalue of the rate-of-strain tensor. This phenomenon, known as vorticity alignment, represents a remarkable orientational order in the fully developed random field. Since its discovery in a direct numerical simulation (DNS) by Ashurst et al. (1987), various scenarios for this alignment have been proposed. However, its precise mechanism remains elusive.In this study, we propose to describe the alignment property using local spherical coordinates defined by the eigen-directions (principal axes) of the rate-of-strain tensor. Using these coordinates we revisit the three-dimensional structure of the alignment property. This revision leads us to develop a dynamical-system model to describe the orientation of the vorticity. We then show that the vorticity alignment in question corresponds to a quasi-equilibrium point of the model. Lastly, returning to DNS , we statistically analyse vortical structures in the local coordinates to identify the structure responsible for the vorticity alignment.