A vortex identification method based on local fluid rotation

Abstract

In this work, a vortex identification method is developed by analyzing the physical meaning of the local rotation of fluid elements. It is shown that a point is locally rotational when the velocity gradient tensor at the point has a pair of complex eigenvalues. The local rotation can be represented by a so called vortex vector. The direction of the vortex vector is defined as that of the local fluid rotation axis, which is parallel to the eigenvector of velocity gradient tensor corresponding to the real eigenvalue. The magnitude is evaluated as the twice of the minimum angular velocity around the point among all azimuth in the plane perpendicular to the vortex vector. Based on the local fluid rotation, a vortex is identified as a connected region where the vortex vector at each point is not equal to zero. The vortex identification method is validated by applying it to Reynolds-averaged Navier-Stokes data and direct numerical simulation data. The results reveal that the method can fully describe the complex structures of vortices.