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.

Why current-carrying magnetic flux tubes gobble up plasma and become thin as a result

“…which shows that B φ must increase since ∇ • U pol < 0 (we note that amplification of a magnetic field by a converging flow has previously been discussed in Ref. [26] but has not otherwise received much attention). In the vicinity of the stagnation layer at z = 0, the continuity equation reduces to 1 ρ…”

Effect of orientation dynamics on the growth of a passive vector in a family of model flows

“…In the kinematic model, the flowfield is given-most often analytically-and used to derive the magnetic field from the induction equation; see for instance Courvoisier et al (2005) and Galloway (2012) for a review of the most current model flows. Now, while the passive vector alignments have been investigated in turbulent flows (Ohkitani 2002, Tsinober andGalanti 2003), it appears that a few studies devoted to the dynamo effect specifically deal with the alignment properties of the magnetic field vector (Brandenburg 1995, Polygiannakis andMoussas 1999).…”

Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

“…The bare kinematics of vector amplification -in non-diffusive tracer advection, kinematic dynamo, or inviscid vortex stretching -is a matter of strain level and orientation within the strain eigenframe. Just like strain intensity, vector orientation is essential to the process and was investigated in many studies [3][4][5][6][7] (see [2] for more references).…”