On the role of strain rate and vorticity in plasmas

Abstract

It is shown that the magnetic field's local evolution in plasmas is directly affected by an interplay between the deformation (strain rate) and the self-rotation (vorticity) of the elementary plasma fluid volumes. At regions of strong strain rate, the fast local convergence or divergence of the flow causes exponential increase or decrease of the field's components, respectively. At regions of strong vorticity, faster directional than magnitude variations of the field occur, explaining the field alignment of the field minimum-variance direction and the random wandering of the field's tip on a sphere, both observed in the solar wind plasma, even in the absence of Alfvén waves. We further investigate the coupling between the maximum strain-rate direction and the local magnetic field, that was previously deduced from magnetic field measurements in the outer heliosphere. Cases of long-lasting, non-Parkerian, radial heliospheric magnetic field are also shown to be periods of field-aligned strain rate. A statistical proof for this alignment is given, assuming that the small-scale field fluctuations are weakly stationary and time reversible. We further propose a generalization of the Stokesian fluid stress-strain relation to the case of one-fluid, collisionless MHD plasmas, including the effects of turbulent viscosity and magnetically induced shearing motion. For a negligible or isotropic or `field-aligned' thermal pressure tensor, the proposed `Stokesian plasma' relation implies the field alignment of the solar wind plasma strain-rate direction and leads to anisotropic stress-strain balance equations, related to those of `firehose' plasma instability. The field alignment of a principal strain-rate direction leads to simplifications in the magnetic-induction equation, especially in the case of force-free fields. For the simplified case of homogeneous, isotropic and incompressible plasma turbulence, the proposed stress-strain-rate relation implies that the velocity and magnetic field inertial range spectra should be identical, further reducing to the Kolmogorov-like k-5/3 law for scale-invariant eddy cascade at constant energy-dissipation rate.