2,611 research outputs found
Dissipative and nonaxisymmetric standard-MRI in Kepler disks
Deviations from axial symmetry are necessary to maintain self-sustained
MRI-turbulence. We define the parameters region where nonaxisymmetric MRI is
excited and study dependence of the unstable modes structure and growth rates
on the relevant parameters. We solve numerically the linear eigenvalue problem
for global axisymmetric and nonaxisymmetric modes of standard-MRI in Keplerian
disks with finite diffusion. For small magnetic Prandtl number the microscopic
viscosity completely drops out from the analysis so that the stability maps and
the growth rates expressed in terms of the magnetic Reynolds number Rm and the
Lundquist number S do not depend on the magnetic Prandtl number Pm. The minimum
magnetic field for onset of nonaxisymmetric MRI grows with Rm. For given S all
nonaxisymmetric modes disappear for sufficiently high Rm. This behavior is a
consequence of the radial fine-structure of the nonaxisymmetric modes resulting
from the winding effect of differential rotation. It is this fine-structure
which presents severe resolution problems for the numerical simulation of MRI
at large Rm. For weak supercritical magnetic fields only axisymmetric modes are
unstable. Nonaxisymmetric modes need stronger fields and not too fast rotation.
If Pm is small its real value does not play any role in MRI.Comment: 4 pages, 6 figures, A&A Lette
Helicity and alpha-effect by current-driven instabilities of helical magnetic fields
Helical magnetic background fields with adjustable pitch angle are imposed on
a conducting fluid in a differentially rotating cylindrical container. The
small-scale kinetic and current helicities are calculated for various field
geometries, and shown to have the opposite sign as the helicity of the
large-scale field. These helicities and also the corresponding -effect
scale with the current helicity of the background field. The -tensor is
highly anisotropic as the components and have
opposite signs. The amplitudes of the azimuthal -effect computed with
the cylindrical 3D MHD code are so small that the operation of an
dynamo on the basis of the current-driven, kink-type
instabilities of toroidal fields is highly questionable. In any case the low
value of the -effect would lead to very long growth times of a dynamo
in the radiation zone of the Sun and early-type stars of the order of
mega-years.Comment: 6 pages, 7 figures, submitted to MNRA
The angular momentum transport by standard MRI in quasi-Kepler cylindric Taylor-Couette flows
The instability of a quasi-Kepler flow in dissipative Taylor-Couette systems
under the presence of an homogeneous axial magnetic field is considered with
focus to the excitation of nonaxisymmetric modes and the resulting angular
momentum transport. The excitation of nonaxisymmetric modes requires higher
rotation rates than the excitation of the axisymmetric mode and this the more
the higher the azimuthal mode number m. We find that the weak-field branch in
the instability map of the nonaxisymmetric modes has always a positive slope
(in opposition to the axisymmetric modes) so that for given magnetic field the
modes with m>0 always have an upper limit of the supercritical Reynolds number.
In order to excite a nonaxisymmetric mode at 1 AU in a Kepler disk a minimum
field strength of about 1 Gauss is necessary. For weaker magnetic field the
nonaxisymmetric modes decay. The angular momentum transport of the
nonaxisymmetric modes is always positive and depends linearly on the Lundquist
number of the background field. The molecular viscosity and the basic rotation
rate do not influence the related {\alpha}-parameter. We did not find any
indication that the MRI decays for small magnetic Prandtl number as found by
use of shearing-box codes. At 1 AU in a Kepler disk and a field strength of
about 1 Gauss the {\alpha} proves to be (only) of order 0.005
Stratorotational instability in Taylor-Couette flow heated from above
We investigate the instability and nonlinear saturation of
temperature-stratified Taylor-Couette flows in a finite height cylindrical gap
and calculate angular-momentum transport in the nonlinear regime. The model is
based on an incompressible fluid in Boussinesq approximation with a positive
axial temperature gradient applied. While both ingredients itself, the
differential rotation as well as the stratification due to the temperature
gradient, are stable, together the system becomes subject of the
stratorotational instability and nonaxisymmetric flow pattern evolve. This flow
configuration transports angular momentum outwards and will therefor be
relevant for astrophysical applications. The belonging viscosity
coefficient is of the order of unity if the results are adapted to the size of
an accretion disc. The strength of the stratification, the fluids Prandtl
number and the boundary conditions applied in the simulations are well-suited
too for a laboratory experiment using water and a small temperature gradient
below five Kelvin. With such a rather easy realizable set-up the SRI and its
angular momentum transport could be measured in an experiment.Comment: 10 pages, 6 figures, revised version appeared in J. Fluid Mech.
(2009), vol. 623, pp. 375--38
Stability of latitudinal differential rotation in stars
The question is addressed whether stellar differentially rotating radiative
zones (like the solar tachocline) excite nonaxisymmetric r-modes which can be
observed. To this end the hydrodynamical stability of latitudinal differential
rotation is studied. The amount of rotational shear required for the
instability is estimated in dependence of the character of radial
stratification and the flow patterns excited by the instability are found. The
eigenvalue equations for the nonaxisymmetric disturbances are formulated in 3D
and then solved numerically. Radial displacements and entropy disturbances are
included. The equations contain the 2D approximation of strictly horizontal
displacements as a special limit. The critical magnitude of the latitudinal
differential rotation for onset of the instability is considerably reduced in
the 3D theory compared to the 2D approximation. The instability requires a
subadiabatic stratification. It does not exist in the bulk of convection zone
with almost adiabatic stratification but may switch on near its base in the
region of penetrative convection. Growth rates and symmetry types of the modes
are computed in dependence on the rotation law parameters. The S1 mode with its
transequatorial toroidal vortices is predicted as the dominating instability
mode. The vortices show longitudinal drift rates retrograde to the basic
rotation which are close to that of the observed weak r-mode signatures at the
solar surface.Comment: 5 pages, 6 figure
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