The invariants of the velocity gradient tensor in turbulence offer a compact description of local kinematics and flow topology. For incompressible magnetohydrodynamic turbulence, analysis of the second and third invariants (Q, R) of the velocity gradient tensor clarifies how coherent structures are organized and evolve. Extending the same analysis to the magnetic field gradient tensor provides additional information on the dynamics. In this study, pseudo-spectral simulation is used to obtain the velocity and magnetic field of the turbulent flow, and analysis of the flow field is conducted through joint probability density functions (PDFs) of the invariants. Furthermore, we explore the influence of the external mean magnetic field strength, B0. The results show that when an external magnetic field is present, the Q–R joint PDF no longer maintains the familiar teardrop distribution for the velocity field, and the flow field structure tends to be two-dimensional with increasing B0. For the fluctuation magnetic field, the Q–R joint PDF takes on a “cigar” shape that becomes more elongated as B0 increases. Moreover, as the strength of the external mean magnetic field increases, the turbulence exhibits enhanced small-scale dissipation and localization, accompanied by a reduction in the effective dimensionality of the system toward a quasi-two-dimensional regime.
Gao et al. (Sun,) studied this question.