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| last change Sat, 12 Mar 2011 11:52:50 GMT, U. Hanschur |
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Magnetohydrodynamics |
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Radial profiles of the alpha-effect, for which a spherical alpha^2 mean-field dynamo yields oscillating solutions. The profile has to be within the grey channel to produce oscillations.
Graph: A. Giesecke
[web size] [full size]
more at /highlight_archive/giesecke2/index.html (image added 2006-01-31) |
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Radial profiles of the alpha-effect, for which a spherical alpha^2 mean-field dynamo yields oscillating solutions. The profile has to be within the grey channel to produce oscillations.
Graph: A. Giesecke
[web size] [full size]
more at /highlight_archive/giesecke2/index.html (image added 2006-01-31) |
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The convection in the outer core of the Earth can lead to irregular magnetic field reversals. This is simulated by a statistically fluctuating zero of the alpha-effect in a full-sphere computation. The left panel shows the 'active' shell corresponding to the yellow-lilac area above, but now showing the strength of the magnetic field. The upper right panel gives the fluctuation of the ?-distribution. The dashed lines indicate the very narrow channel in which oscillatory solutions can occur. The lower right panel measures the magnetic field at the north pole. The polarity is constant over long periods of time, but occasionally it is changed. (MPEG, 16MB)
Simulation and graphics: A. Giesecke
more at http://www.aip.de/highlight_archive/giesecke2/ (image added 2005-02-22) |
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Magnetic star-disk interaction
A classical T Tauri star is a pre-main sequence star surrounded by an accretion disk. Magnetic fields are thought to play a crucial part in the angular momentum evolution of the star. They can directly transfer angular momentum between star and disk, and also drive outflows. Computer simulations show how an initially dipolar field interacts with the accretion disk.
The images show the density distribution, magnetic field lines (solid lines), and gas motion (velocity vectors) in the volume surrounding the star. The left margin of each image is the stellar rotation axis. The left picture shows the initial configuration, the right picture the state that has evolved after about 100 orbits of the inner boundary of the disk. The original dipole is wound up due to the different rotation rates of the footpoints of each field line. The resulting magnetocentrifugal force drives part of the gas outwards and the dipole is replaced with an open field line configuration.
by courtesy of Manfred Küker
more at http://www.aip.de/groups/MHD/ (image added 2002-12-04) |
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Global accretion-disk simulations
High luminosity and short time-scales of variability are typical for disks which collect matter from the surroundings to accrete the gas and dust onto a central object. The efficiency of that transport requires turbulence in the disk. Searches for instabilities in such accretion disks revealed the magneto-rotational instability as a powerful mechanism in a wide range of objects (protostellar disks, cataclysmic binaries, active galactic nuclei): A weak magnetic fields threads a differentially rotating disk and excites an instability.
The global simulation of such disk configurations on a computer are a challenge for modern computational astrophysics. The image shows five horizontal slices through a simulated accretion disk at five different height levels. The middle slice is the equatorial plane. The colour shading represents the density.
The tubulent flows in the simulated disks turn out to provide powerful transport as required to match the observed phe nomena. Additional generation of strong, large-scale magnetic fields may further illuminate our understanding of what is called dynamo action and the launch of collimated outflows (jets) from the disk as observed in protostellar disks and active galactic nuclei.
(credits: R. Arlt, G. Rüdiger)
more at http://www.aip.de/~rarlt/ (image added 2002-12-04) |
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Numerical simulation of a magnetically driven outflow (jet)
Jets are ejected from young stellar objects as well from
active galactic nuclei. The matter being accelerated
originates from the disk around the star/black hole
accreting matter from the surroundings.
Colours indicate density, increasing from blue to yellow.
The numerical resolution is 900 times 200 grid cells.
Lines denote twenty linearly spaced magnetic flux surfaces
The jet is shown after 400 rotations of the underlying
accretion disk.
credits: M. Cemeljic
more at http://www.aip.de/groups/MHD/ (image added 2002-12-10) |
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Taylor-Couette experiment
The gap between two co-rotating cylinders is filled
with a fluid. The inner cylinder rotates with a
period different from the outer cylinder. If the
inner cylinder is fast enough, the fluid becomes
turbulent. Otherwise the flow is laminar. The presence
of a magnetic field B can enhance the onset of
turbulence. The setup is similar to the rotation
of protostellar disks.
A. Ritter, G. Rüdiger
more at http://www.aip.de/groups/MHD/ (image added 2003-01-23) |
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The missing chapter in Chandrasekhar's book
...would have been about the magneto-rotational instability. The transport of specific angular momentum is a delicate problem in various astronomical objects. The formation of stars and planets as well as the rotation of stellar interiors, also the luminosity of galactic nuclei imply transporting angular momentum inside out. Instabilities may provide such transport.
Cosmic rotation curves are not easily accessible to terrestrial experiments. A close analogue is the Taylor-Couette flow - a fluid between rotating cylinders. If the rotation speed of the cylinders differs a lot, the flow is unstable for higher than a critical Reynolds number. Chandrasekhar studied such a flow with magnetic fields and could not find an earlier onset of instability. He actually made an approximation valid for very low ratios of viscosity to diffusivity (magn. Prandtl number, upper curves in the graph, the Hartmann number is a measure of the magnetic field strength).
Now we studied MHD Taylor-Couette flows for large Prandtl numbers, and there is indeed a subcritical excitation of Taylor vortices due to the presence of magnetic fields. The graphs for Prandtl number = 1 and = 10 have a minimum. The magnetic Prandtl numbers in astrophysical objects are indeed orders of magnitudes larger than those of terrestrial conducting fluids (Hg 10^-7, Ga 10^-6, Na 10^-5).
Other than in this experimental Taylor-Couette flow, astrophysical rotation profiles are hydrodynamically very stable. The magnetic fields will be essential for angular-momentum transport. The Taylor-Couette flow may, however, be a chance to see the magneto-rotational instability in experiments. First projects are being started to get cosmic objects into the laboratory!
(credits: G. Rüdiger, R. Arlt, AIP)
more at http://www.aip.de/groups/MHD/ (image added 2002-12-04) |
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![[full size]](images/giesecke_alpha_1_xl.gif){kind=link}
![[full size]](images/giesecke_alpha_2_xl.gif){kind=link}