Identifying 3‐D Vortex Structures At/Around the Magnetopause Using a Tetrahedral Satellite Configuration

Identifying vortices is the key to understanding the turbulence in plasma shear layers. This paper aims to provide general guidelines for identifying 3‐D vortex structures. Currently, no single precise definition of a vortex is universally accepted, despite the significance of vortices in fluid and plasma dynamics. Recently, various vortex identification methods using Galilean invariance have been proposed by numerous researchers. These methods are general for different fluid and plasma visualization applications. In the present paper, we describe how we have identified 105 vortex structures by applying these methods to Cluster data near the duskside of the magnetopause. Four sets of Cluster satellite magnetic field data are used to linearly approximate the magnetic field. We identify the 3‐D magnetic vortex structures by using various vortex identification criteria as follows: (i) the first criterion is Q‐criterion that defines vortices as regions in which the vorticity energy prevails over other energies; (ii) the second criterion is the λ 2 ‐criterion that is related to the minus eigenvalue of the Hessian matrix of the pressure terms; and (iii) the third criterion called the geometrical line‐type method requires the existence of Galilean‐invariant vortex core inside the four Cluster tetrahedral regions. In reality, both Q‐ and λ 2 ‐criteria are also related to Galilean invariance. The present analysis evidences that the geometrical line‐type method is more precise than the other two using Cluster satellite magnetic field data.