Issue |
A&A
Volume 378, Number 1, October IV 2001
|
|
---|---|---|
Page(s) | 302 - 308 | |
Section | Astronomical instrumentation | |
DOI | https://doi.org/10.1051/0004-6361:20011214 | |
Published online | 15 October 2001 |
MHD instability in differentially-rotating cylindric flows
Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
Corresponding author: G. Rüdiger, gruediger@aip.de
Received:
28
March
2001
Accepted:
24
August
2001
The possibility that the magnetic shear-flow instability (MRI, also Balbus-Hawley instability) might give rise to turbulence in
a cylindrical Couette flow is investigated through numerical
simulations. The study is linear and the fluid is assumed
to be incompressible and differentially rotating with the
rotation law .
The model is fully global in all three spatial directions
with boundaries on each side; finite diffusivities are also
imposed. The computations are carried out for several
values of the azimuthal wavenumber m of the perturbations in order
to analyze whether or not non-axisymmetric modes are preferred,
which in a nonlinear extension of the study finally might lead to
a dynamo-generated magnetic field.
For magnetic Prandtl number of order unity we find that with a magnetic field the instability is generally easier to
excite than without a magnetic field. The critical Reynolds number for
Pm = 1 is of the order of 50, independent of whether or not the nonmagnetic flow is stable. We find that i) the magnetic field strongly reduces the number of
Taylor vortices, ii) the angular momentum is transported outwards and iii) for finite cylinders a net
dynamo-alpha effect results which is negative (positive) for the upper (lower) part of the cylinder.
For magnetic Prandtl number smaller than unity the critical Reynolds
number appears to scale with Pm-0.65. If this was true even for very small
magnetic Prandtl numbers (e.g. for 10-5, the magnetic Prandtl number of liquid sodium) the critical Reynolds number
should reach the value of 105 which, however, is also characteristic of the nonlinear finite-amplitude hydrodynamic
Taylor-Couette turbulence
-so that we have to expect the simultaneous existence
of both sorts of instabilities in related experiments. Similar phenomena are also discussed for cold accretion disks with their basically small magnetic Prandtl numbers.
Key words: magnetohydrodynamics / accretion, accretion disks / turbulence
© ESO, 2001
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