On Schur Decomposition of Magnetic and Velocity Gradient Tensors in Space Plasma Turbulence

The study of the statistics of gradient tensors' invariants is useful to characterize the morphological/topological features of magnetic flux and plasma velocity flow lines in turbulent space plasmas. In the recent past, some studies of the statistics of the gradient tensors' invariants have been done to investigate the velocity and magnetic field flow lines topologies in turbulent heliospheric plasmas, thanks to the availability of multipoint missions. Here, we present a novel/complementary approach to the characterization of the gradient tensor properties of velocity and magnetic field in plasmas based on Schur decomposition of the field gradient tensors. This decomposition can be seen as an alternative to the standard decomposition into symmetric and skew-symmetric components, allowing for a decomposition of gradients into normal and nonnormal parts, separating eigenvalue and ideal pressure terms from the deviatoric and dissipative ones. The method is preliminarily applied to observations from the NASA Magnetospheric Multiscale space mission in the solar wind and the magnetosheath to show its potentiality.