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Register a new userActive modes and dynamical balances in MRI-turbulence of Keplerian disks with a net vertical magnetic field
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Added by
George Mamatsashvili
Publication date
2018
fields
Physics
and research's language is
English
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We studied dynamical balances in magnetorotational instability (MRI) turbulence with a net vertical field in the shearing box model of disks. Analyzing the turbulence dynamics in Fourier (${bf k}$-)space, we identified three types of active modes that define turbulence characteristics. These modes have lengths similar to the box size, i.e., lie in the small wavenumber region in Fourier space labeled the vital area and are: (i) the channel mode - uniform in the disk plane with the smallest vertical wavenumber,(ii) the zonal flow mode - azimuthally and vertically uniform with the smallest radial wavenumber and (iii) the rest modes. The rest modes comprise those harmonics in the vital area whose energies reach more than $50 %$ of the maximum spectral energy. The rest modes individually are not so significant compared to the channel and zonal flow modes, however, the combined action of their multitude is dominant over these two modes. These three mode types are governed by interplay of the linear and nonlinear processes, leading to their interdependent dynamics. The linear processes consist in disk flow nonmodality-modified classical MRI with a net vertical field. The main nonlinear process is transfer of modes over wavevector angles in Fourier space - the transverse cascade. The channel mode exhibits episodic bursts supplied by linear MRI growth, while the nonlinear processes mostly oppose this, draining the channel energy and redistributing it to the rest modes. As for the zonal flow, it does not have a linear source and is fed by nonlinear interactions of the rest modes.
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We investigate sustenance and dependence on magnetic Prandtl number (${rm Pm}$) for magnetorotational instability (MRI)-driven turbulence in astrophysical Keplerian disks with zero net magnetic flux using standard shearing box simulations. We focus on the turbulence dynamics in Fourier space, capturing specific/noncanonical anisotropy of nonlinear processes due to disk flow shear. This is a new type of nonlinear redistribution of modes over wavevector orientations in Fourier space -- the nonlinear transverse cascade -- which is generic to shear flows and fundamentally different from usual direct/inverse cascade. The zero flux MRI has no exponentially growing modes, so its growth is transient, or nonmodal. Turbulence self-sustenance is governed by constructive cooperation of the transient growth of MRI and the nonlinear transverse cascade. This cooperation takes place at small wavenumbers (on the flow size scales) referred to as the vital area in Fourier space. The direct cascade transfers mode energy from the vital area to larger wavenumbers. At large ${rm Pm}$, the transverse cascade prevails over the direct one, keeping most of modes energy contained in small wavenumbers. With decreasing ${rm Pm}$, however, the action of the transverse cascade weakens and can no longer oppose the action of direct cascade which more efficiently transfers energy to higher wavenumbers, leading to increased resistive dissipation. This undermines the sustenance scheme, resulting in the turbulence decay. Thus, the decay of zero net flux MRI-turbulence with decreasing ${rm Pm}$ is attributed to topological rearrangement of the nonlinear processes when the direct cascade begins to prevail over the transverse cascade.
We study wakes and gap opening by low mass planets in gaseous protoplanetary disks threaded by net vertical magnetic fields which drive magnetohydrodynamical (MHD) turbulence through the magnetorotational instabilty (MRI), using three dimensional simulations in the unstratified local shearing box approximation. The wakes, which are excited by the planets, are damped by shocks similar to the wake damping in inviscid hydrodynamic (HD) disks. Angular momentum deposition by shock damping opens gaps in both MHD turbulent disks and inviscid HD disks even for low mass planets, in contradiction to the thermal criterion for gap opening. To test the viscous criterion, we compared gap properties in MRI-turbulent disks to those in viscous HD disks having the same stress, and found that the same mass planet opens a significantly deeper and wider gap in net vertical flux MHD disks than in viscous HD disks. This difference arises due to the efficient magnetic field transport into the gap region in MRI disks, leading to a larger effective alpha within the gap. Thus, across the gap, the Maxwell stress profile is smoother than the gap density profile, and a deeper gap is needed for the Maxwell stress gradient to balance the planetary torque density. We also confirmed the large excess torque close to the planet in MHD disks, and found that long-lived density features (termed zonal flows) produced by the MRI can affect planet migration. The comparison with previous results from net toroidal flux/zero flux MHD simulations indicates that the magnetic field geometry plays an important role in the gap opening process. Overall, our results suggest that gaps can be commonly produced by low mass planets in realistic protoplanetary disks, and caution the use of a constant alpha-viscosity to model gaps in protoplanetary disks.
In this paper we consider two outstanding intertwined problems in modern high-energy astrophysics: (1) the vertical thermal structure of an optically thick accretion disk heated by the dissipation of magnetohydrodynamic (MHD) turbulence driven by the magneto-rotational instability (MRI), and (2) determining the fraction of the accretion power released in the corona above the disk. For simplicity, we consider a gas-pressure-dominated disk and assume a constant opacity. We argue that the local turbulent dissipation rate due to the disruption of MRI channel flows by secondary parasitic instabilities should be uniform across most of the disk, almost up to the disk photosphere. We then obtain a self-consistent analytical solution for the vertical thermal structure of the disk, governed by the balance between the heating by MRI turbulence and the cooling by radiative diffusion. Next, we argue that the coronal power fraction is determined by the competition between the Parker instability, viewed as a parasitic instability feeding off of MRI channel flows, and other parasitic instabilities. We show that the Parker instability inevitably becomes important near the disk surface, leading to a certain lower limit on the coronal power. While most of the analysis in this paper focuses on the case of a disk threaded by an externally imposed vertical magnetic field, we also discuss the zero-net-flux case, in which the magnetic field is produced by the MRI dynamo itself, and show that most of our arguments and conclusions should be valid in this case as well.
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The stationary accretion shock instability (SASI) plays a central role in modern simulations of the explosion phase of core-collapse supernovae (CCSNe). It may be key to realizing neutrino powered explosions, and possibly links birth properties of pulsars (e.g., kick, spin, and magnetic field) to supernova dynamics. Using high-resolution magnetohydrodynamic simulations, we study the development of turbulence, and subsequent amplification of magnetic fields in a simplified model of the post-bounce core-collapse supernova environment. Turbulence develops from secondary instabilities induced by the SASI. Our simulations suggest that the development of turbulence plays an important role for the subsequent evolution of the SASI. The turbulence also acts to amplify weak magnetic fields via a small-scale dynamo.
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