Zero net flux MRI-turbulence in disks – specific anisotropy of nonlinear processes, sustenance and dependence on magnetic Prandtl number

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• George Mamatsashvili - Helmholtz-Zentrum Dresden-Rossendorf
• Monday 26 April 2021, 14:00-15:00
• Online.

If you have a question about this talk, please contact Cleo Loi.

We study the sustenance and effect of magnetic Prandtl (Pm) number for MRI -turbulence in accretion disks with a zero net magnetic flux in the shearing-box. The zero flux case is unique, as there is no characteristic length-scale for MRI that would grow purely exponentially and hence the instability is instead of a subcritical type, being energetically powered by linear nonmodal/transient mechanism of perturbation growth. This transient growth of MRI is “imperfect” in the sense that it is not able to ensure long-term sustenance of the turbulence. This should be compensated by a necessary positive nonlinear feedback, regenerating nonmodally growing MRI modes. To examine the existence of such a feedback and ultimately understand the self-sustenance process, we first perform numerical simulations with SNOOPY code and then do a detailed analysis of the turbulence dynamics in Fourier space. Our main results can be summarized as:

1. It was shown that the flow shear leads to anisotropy of nonlinear processes in Fourier space. A key factor for the sustenance is the existence and dominance of a topologically new type of a nonlinear process – an angular (i.e., over wavevector orientations) redistribution of modes in Fourier space, which we call the nonlinear transverse cascade in contrast to the classical direct/inverse cascade in classical (Kolmogorov, Iroshnikov-Kraichnan) theories of isotropic turbulence without mean shear flow. The transverse cascade that we revealed is the generic nonlinear process of decisive importance in different kinds of shear flows.

2. The sustenance of the MRI -turbulence is achieved by the interplay of the linear nonmodal growth of MRI and the nonlinear transverse cascade. These two processes mainly operate at length scales comparable to the box size (disk scale height) which we refer to as the vital area of the turbulence in Fourier space. The usual direct cascade merely transfers the energy of these modes from the vital area to large dissipative wavenumbers (small scales).

3. At large Pm, the transverse cascade prevails over the direct one, keeping most of the mode energy contained in small wavenumber (large scales) modes. With decreasing Pm, the action of the nonlinear transverse cascade weakens, so that it can no longer oppose the action of the direct cascade, which transfers energy of small wavenumber modes to higher wavenumber ones, where it is efficiently dissipated, leading to the decay of the turbulence. Thus, decreasing of Pm results in the topological rearrangement of the nonlinear processes when the action of the direct cascade begins to dominate over the action of the key agent for the turbulence sustenance – the nonlinear transverse cascade.

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