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SUMMARY:Zero net flux MRI-turbulence in disks – specific anisotropy of n
 onlinear processes\, sustenance and dependence on magnetic Prandtl number 
 - George Mamatsashvili - Helmholtz-Zentrum Dresden-Rossendorf
DTSTART:20210426T130000Z
DTEND:20210426T140000Z
UID:TALK155902@talks.cam.ac.uk
CONTACT:Cleo Loi
DESCRIPTION:We study the sustenance and effect of magnetic Prandtl (Pm) nu
 mber for\nMRI-turbulence in accretion disks with a zero net magnetic flux 
 in the\nshearing-box. The zero flux case is unique\, as there is no charac
 teristic\nlength-scale for MRI that would grow purely exponentially and he
 nce the\ninstability is instead of a subcritical type\, being energeticall
 y powered by\nlinear nonmodal/transient mechanism of perturbation growth. 
 This transient\ngrowth of MRI is “imperfect” in the sense that it is n
 ot able to ensure\nlong-term sustenance of the turbulence. This  should be
  compensated by a\nnecessary positive nonlinear feedback\, regenerating no
 nmodally growing MRI\nmodes. To examine the existence of such a feedback a
 nd ultimately understand\nthe self-sustenance process\, we first perform n
 umerical simulations with\nSNOOPY code and then do a detailed analysis of 
 the turbulence dynamics in\nFourier space. Our main results can be summari
 zed as:\n\n1. It was shown that the flow shear leads to anisotropy of nonl
 inear processes\nin Fourier space. A key factor for the sustenance is the 
 existence and\ndominance of a topologically new type of a nonlinear proces
 s – an angular\n(i.e.\, over wavevector orientations) redistribution of 
 modes in Fourier space\,\nwhich we call the nonlinear transverse cascade i
 n contrast to the classical\ndirect/inverse cascade in classical (Kolmogor
 ov\, Iroshnikov-Kraichnan)\ntheories of isotropic turbulence without mean 
 shear flow. The transverse\ncascade that we revealed is the generic nonlin
 ear process of decisive\nimportance in different kinds of shear flows.\n\n
 2. The sustenance of the MRI-turbulence is achieved by the interplay of th
 e\nlinear nonmodal growth of MRI and the nonlinear transverse cascade. The
 se two\nprocesses mainly operate at length scales comparable to the box si
 ze (disk\nscale height) which we refer to as the vital area of the turbule
 nce in Fourier\nspace. The usual direct cascade merely transfers the energ
 y of these modes\nfrom the vital area to large dissipative wavenumbers (sm
 all scales).\n\n3. At large Pm\, the transverse cascade prevails over the 
 direct one\, keeping\nmost of the mode energy contained in small wavenumbe
 r (large scales) modes.\nWith decreasing Pm\, the action of the nonlinear 
 transverse cascade weakens\, so\nthat it can no longer oppose the action o
 f the direct cascade\, which transfers\nenergy of small wavenumber modes t
 o higher wavenumber ones\, where it is\nefficiently dissipated\, leading t
 o the decay of the turbulence. Thus\,\ndecreasing of Pm results in the top
 ological rearrangement of the nonlinear\nprocesses when the action of the 
 direct cascade begins to dominate over the\naction of the key agent for th
 e turbulence sustenance - the nonlinear\ntransverse cascade.
LOCATION:Online
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