51 research outputs found
Axisymmetric Magnetorotational Instability in Viscous Accretion Disks
Axisymmetric magnetorotational instability (MRI) in viscous accretion disks
is investigated by linear analysis and two-dimensional nonlinear simulations.
The linear growth of the viscous MRI is characterized by the Reynolds number
defined as , where is the Alfv{\'e}n
velocity, is the kinematic viscosity, and is the angular
velocity of the disk. Although the linear growth rate is suppressed
considerably as the Reynolds number decreases, the nonlinear behavior is found
to be almost independent of . At the nonlinear evolutionary stage,
a two-channel flow continues growing and the Maxwell stress increases until the
end of calculations even though the Reynolds number is much smaller than unity.
A large portion of the injected energy to the system is converted to the
magnetic energy. The gain rate of the thermal energy, on the other hand, is
found to be much larger than the viscous heating rate. Nonlinear behavior of
the MRI in the viscous regime and its difference from that in the highly
resistive regime can be explained schematically by using the characteristics of
the linear dispersion relation. Applying our results to the case with both the
viscosity and resistivity, it is anticipated that the critical value of the
Lundquist number for active turbulence
depends on the magnetic Prandtl number in
the regime of and remains constant when , where and is the magnetic diffusivity.Comment: Accepted for publication in ApJ -- 18 pages, 9 figures, 1 tabl
Modelling stellar convective transport with plumes: I. Non-equilibrium turbulence effect in double-averaging formulation
Plumes in a convective flow are considered to be relevant to the turbulent
transport in convection. The effective mass, momentum, and heat transports in
the convective turbulence are investigated in the framework of time--space
double averaging procedure, where a field quantity is decomposed into three
parts: the spatiotemporal mean (spatial average of the time-averaged) field,
the dispersion or coherent fluctuation, and the random or incoherent
fluctuation. With this framework, turbulent correlations in the mean-field
equations are divided into the dispersion/coherent and random/incoherent
correlation part. By reckoning the plume as the coherent fluctuation, a
transport model for the convective turbulence is constructed with the aid of
the non-equilibrium effect, in which the change of turbulence characteristics
along the mean stream is taken into account for the modelling of the turbulent
transport coefficients. In this work, for the first time, change of turbulence
properties along plume motions is incorporated into the expression of the
turbulent transport coefficients. This non-equilibrium model is applied to a
stellar convective flow. One of the prominent characteristics of a surface
cooling-driven convection, the enhanced and localised turbulent mass flux below
the surface layer, which cannot be reproduced at all by the usual
eddy-diffusivity model with mixing length theory (MLT), is well reproduced by
the present model. Our results show that the incorporation of plume motion into
turbulent transport model is an important and very relevant extension of
mean-field theory beyond the heuristic gradient transport model with MLT.Comment: 18 pages, 8 figure
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