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Title: The small magnetic Prandtl number approximation suppresses magnetorotational instability

Authors:
;
Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES)
OSTI Identifier:
1211638
Resource Type:
Journal Article
Resource Relation:
Journal Name: Zeitschrift fuer Angewandte Mathematik und Physik; Journal Volume: 57; Journal Issue: 4
Country of Publication:
United States
Language:
English

Citation Formats

Herron, I, and Goodman, J. The small magnetic Prandtl number approximation suppresses magnetorotational instability. United States: N. p., 2006. Web. doi:10.1007/s00033-006-0060-y.
Herron, I, & Goodman, J. The small magnetic Prandtl number approximation suppresses magnetorotational instability. United States. doi:10.1007/s00033-006-0060-y.
Herron, I, and Goodman, J. Thu . "The small magnetic Prandtl number approximation suppresses magnetorotational instability". United States. doi:10.1007/s00033-006-0060-y.
@article{osti_1211638,
title = {The small magnetic Prandtl number approximation suppresses magnetorotational instability},
author = {Herron, I and Goodman, J},
abstractNote = {},
doi = {10.1007/s00033-006-0060-y},
journal = {Zeitschrift fuer Angewandte Mathematik und Physik},
number = 4,
volume = 57,
place = {United States},
year = {Thu May 11 00:00:00 EDT 2006},
month = {Thu May 11 00:00:00 EDT 2006}
}
  • A large set of numerical simulations of MHD turbulence induced by the magnetorotational instability is presented. Revisiting the previous survey conducted by Sano et al., we investigate the gas pressure dependence of the saturation level. In ideal MHD simulations, the gas pressure dependence is found to be very sensitive to the choice of numerical scheme. This is because the numerical magnetic Prandtl number varies according to the scheme as well as the pressure, which considerably affects the results. The saturation level is more sensitive to the numerical magnetic Prandtl number than the pressure. In MHD simulations with explicit viscosity andmore » resistivity, the saturation level increases with the physical magnetic Prandtl number, and it is almost independent of the gas pressure when the magnetic Prandtl number is constant. This is indicative of the incompressible turbulence saturated by the secondary tearing instability.« less
  • The magnetorotational instability (MRI) may dominate outward transport of angular momentum in accretion disks, allowing material to fall onto the central object. Previous work has established that the MRI can drive a mean-field dynamo, possibly leading to a self-sustaining accretion system. Recently, however, simulations of the scaling of the angular momentum transport parameter {alpha}{sub SS} with the magnetic Prandtl number Pm have cast doubt on the ability of the MRI to transport astrophysically relevant amounts of angular momentum in real disk systems. Here, we use simulations including explicit physical viscosity and resistivity to show that when vertical stratification is included,more » mean field dynamo action operates, driving the system to a configuration in which the magnetic field is not fully helical. This relaxes the constraints on the generated field provided by magnetic helicity conservation, allowing the generation of a mean field on timescales independent of the resistivity. Our models demonstrate the existence of a critical magnetic Reynolds number Rm{sub crit}, below which transport becomes strongly Pm-dependent and chaotic, but above which the transport is steady and Pm-independent. Prior simulations showing Pm-dependence had Rm < Rm{sub crit}. We conjecture that this steady regime is possible because the mean field dynamo is not helicity-limited and thus does not depend on the details of the helicity ejection process. Scaling to realistic astrophysical parameters suggests that disks around both protostars and stellar mass black holes have Rm >> Rm{sub crit}. Thus, we suggest that the strong Pm dependence seen in recent simulations does not occur in real systems.« less
  • The magnetorotational instability (MRI) may dominate outward transport of angular momentum in accretion disks, allowing material to fall onto the central object. Previous work has established that the MRI can drive a mean-field dynamo, possibly leading to a self-sustaining accretion system. Recently, however, simulations of the scaling of the angular momentum transport parameter {alpha}{sub SS} with the magnetic Prandtl number Pm have cast doubt on the ability of the MRI to transport astrophysically relevant amounts of angular momentum in real disk systems. Here, we use simulations including explicit physical viscosity and resistivity to show that when vertical stratification is included,more » mean-field dynamo action operates, driving the system to a configuration in which the magnetic field is not fully helical. This relaxes the constraints on the generated field provided by magnetic helicity conservation, allowing the generation of a mean field on timescales independent of the resistivity. Our models demonstrate the existence of a critical magnetic Reynolds number Rm{sub crit}, below which transport becomes strongly Pm-dependent and chaotic, but above which the transport is steady and Pm-independent. Prior simulations showing Pm dependence had Rm < Rm{sub crit}. We conjecture that this steady regime is possible because the mean-field dynamo is not helicity-limited and thus does not depend on the details of the helicity ejection process. Scaling to realistic astrophysical parameters suggests that disks around both protostars and stellar mass black holes have Rm >> Rm{sub crit}. Thus, we suggest that the strong Pm dependence seen in recent simulations does not occur in real systems.« less
  • The authors present a BGK-type collision model which approximates, by a Chapman-Enskog expansion, the compressible Navier-Stokes equations with a Prandtl number that can be chosen arbitrarily between 0 and 1. This model has the basic properties of the Boltzmann equation, including the H-theorem, but contains an extra parameter in comparison with the standard BGK model. This parameter is introduced multiplying the collision operator by a nonlinear functional of the distribution function. It is adjusted to the Prandtl number. 17 refs.