On Geometrical Invariants of the Magnetic Field Gradient Tensor in Turbulent Space Plasmas: Scale Variability in the Inertial Range

In a recent paper, Consolini et al. investigated the statistics of geometrical invariants of the coarse-grained gradient tensor of plasma velocity for a case study of space plasma turbulence. They showed how, at spatial scales near the proton inertial length, there is evidence for the occurrence of dissipation structures along the Vieillefosse's tail. Here, we extend the previous analysis to the statistics of the geometrical invariants of the magnetic field coarse-grained gradient tensor, computed using magnetic field measurements by the ESA-Cluster mission in the solar wind region. In detail, we investigate the evolution of the joint probability distribution functions of the magnetic geometrical invariants at different scales in the inertial range of turbulent solar wind. The results show a clear dependence of the joint statistics of geometrical invariants on the distance from the proton inertial length scale in the inertial range, which seems to be compatible with a variation of the dimensionality of the fluctuation field from two dimensions to three dimensions at the smallest scales. Evidence of an increasing role of the ingoing spiral saddle and current-associated dissipation structures is found at the smallest investigated scales, where dissipation can occur.