Nonhelical Inverse Transfer of a Decaying Turbulent Magnetic Field

In the presence of magnetic helicity, inverse transfer from small to large scales is well known in magnetohydrodynamic (MHD) turbulence and has applications in astrophysics, cosmology, and fusion plasmas. Using high resolution direct numerical simulations of magnetically dominated self-similarly decaying MHD turbulence, we report a similar inverse transfer even in the absence of magnetic helicity. We compute for the first time spectral energy transfer rates to show that this inverse transfer is about half as strong as with helicity, but in both cases the magnetic gain at large scales results from velocity at similar scales interacting with smaller-scale magnetic fields. This suggests that both inverse transfers are a consequence of universal mechanisms for magnetically dominated turbulence. Possible explanations include inverse cascading of the mean squared vector potential associated with local near two dimensionality and the shallower $k^2$ subinertial range spectrum of kinetic energy forcing the magnetic field with a $k^4$ subinertial range to attain larger-scale coherence. The inertial range shows a clear $k^{-2}$ spectrum and is the first example of fully isotropic magnetically dominated MHD turbulence exhibiting weak turbulence scaling.

Figure 1

(a) Magnetic (solid lines) and kinetic (dashed lines) energy spectra for Run $A$ at times $t/{\tau }_A=18$, 130, 450, and 1800; the time $t/{\tau }_A=450$ is shown as bold lines. The straight lines indicate the slopes $k^4$ (solid blue line), $k^2$ (dashed blue line), and $k^{-2}$ (solid red line). (b) The same for Run $B$, at $t/{\tau }_A=540$, 1300, and 1800, with $t/{\tau }_A=1300$ shown as bold lines. The insets show $E_M$ and $E_K$ compensated by $E_{\text{WT}}$.

Figure 2

Contours of (a) $B_z(x,y)$ and (b) $u_z(x,y)$ for Run $A$. The insets show a zoom into the small square in the lower left corner.

Figure 3

Spectral transfer function $T_{kpq}$, (a) as a function of $k$ and summed over all $p$ and $q$, (b) as a function of $p$ and $q$ for $k/k_1=4$, and (c) as a function of $k$ and $q$ for $p/k_1=4$. The dashed line in (a) and the insets in (b) and (c) show the corresponding case for a DNS with helicity, both for ${\mathrm{Pr}}_M$.

Figure 4

Time evolution of ${\xi }_M=k_M^{-1}$ and ${\xi }_M^{\min }$, as well as the Taylor microscale ${\xi }_{\text{Tay}}$. Fat (thin) lines are for Run $A$ ($B$).