http://arxiv.org/abs/1612.07604
We propose a mechanism whereby the intense, sheetlike structures naturally formed by dynamically aligning Alfv\’enic turbulence are destroyed by magnetic reconnection at a scale $\hat{\lambda}_{\rm D}$, larger than the dissipation scale predicted by models of intermittent, dynamically aligning turbulence. The reconnection process proceeds in several stages: first, a linear tearing mode with $N$ magnetic islands grows and saturates, and then the $X$-points between these islands collapse into secondary current sheets, which then reconnect until the original structure is destroyed. This effectively imposes an upper limit on the anisotropy of the structures within the perpendicular plane, which means that at scale $\hat{\lambda}_{\rm D}$ the turbulent dynamics change: at scales larger than $\hat{\lambda}_{\rm D}$, the turbulence exhibits scale-dependent dynamic alignment and a spectral index approximately equal to $-3/2$, while at scales smaller than $\hat{\lambda}_{\rm D}$ the turbulent structures undergo a succession of disruptions due to the reconnection mechanism, limiting dynamic alignment, steepening the effective spectral index and changing the scaling of the final dissipation scale. The scaling of the transition scale $\hat{\lambda}_{\rm D}$ with the Lundquist (magnetic Reynolds) number $S_{L_\perp}$ depends on the order of the statistics being considered, and on the specific model of intermittency; the transition between the two regimes in the energy spectrum is predicted at approximately $\hat{\lambda}_{\rm D} \sim S_{L_\perp}^{-0.6}$. The final dissipation scale is at $\hat{\lambda}_{\eta,\infty} \sim S_{L_\perp}^{-0.8}$, and may be indistinguishable from the Kolmogorov scale for currently feasible numerical simulations.
A. Mallet, A. Schekochihin and B. Chandran
Fri, 23 Dec 16
7/60
Comments: 9 pages, 3 figures, submitted to MNRAS
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