MRI-turbulence in accretion disks – anisotropic nonlinear transfers, sustenance and dependence on magnetic Prandtl number
George Mamatsashvili, Helmholtz-Zentrum Dresden-Rossendorf — 15.02.2021
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. Zero net flux MRI has attracted great interest and has been very actively studied and debated in the last decade, because it forms the basis of modern nonlinear MRI-dynamo in disks. In the zero flux case, there is no well-defined vertical length-scale for MRI that would grow purely exponentially and hence it should set in instead as a subcritical instability, being energetically powered by linear nonmodal, or transient (that is, taking place on dynamical/orbital timescales) mechanism of perturbation growth. This transient growth of MRI cannot, however, ensure a long-term sustenance of the turbulence. A necessary positive nonlinear feedback is thus required to regenerate nonmodally growing MRI modes. To examine the existence of such a feedback, we performed a detailed analysis of the turbulence dynamics in Fourier/wavenumber space.
It was shown that the flow shear leads to anisotropy of nonlinear processes in Fourier space. As a result, the main nonlinear process appears to be a topologically novel type of angular (i.e., over wavevector orientations) redistribution of modes in Fourier space – referred to as the nonlinear transverse cascade – in contrast to the classical direct/inverse cascade in the absence of shear. Our main finding is that the sustenance of the MRI-turbulence is achieved due to the interplay of the linear nonmodal growth of MRI and the nonlinear transverse cascade. These two processes playing a key role in the sustenance 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). 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 small wavenumber mode energy to higher wavenumber ones. This undermines the overall scheme of the turbulence sustenance and, ultimately, leads to the increased resistive dissipation of the mode energy and to the decay of the turbulence. Thus, the decay of the zero net flux subcritical MRI-turbulence with decreasing Pm is attributed to topological rearrangement of the nonlinear processes when the action of the direct cascade begins to dominate over the action of the nonlinear transverse cascade, which is a key agent for the turbulence sustenance.