On the evolution equations of velocity field gradient tensor invariants in different turbulent heliospheric regions

The characterization of the complex topologies of magnetic and velocity field in turbulent space plasmas benefits from the analysis of the statistics of the gradient tensor invariants. In this work, we evaluate the relative weight of the various terms present in the evolution equation for the velocity (Q and R) and magnetic (X and Y) field gradient tensors invariants, so to establish which is the more appropriate dynamical regime governing the evolution of the magnetic and velocity field line topology. The quantities Q, R, X and Y are related to the characteristic polynomial of the velocity (Q and R quantities) and magnetic (X and Y invariants) fields’ gradient tensors. These four quantities are invariant under transformations of the SO(3)-group. The study is performed using data from both the NASA-MMS mission and direct numerical simulations. In particular, we show how in the solar wind and magnetosheath plasma turbulence the evolution of the velocity field gradient tensor invariants is controlled by different dominant terms. This result is discussed in connection with the different regimes of the observed turbulence, thus providing an alternative approach to the traditional methods used to investigate space plasma turbulence.