Helical dynamos
Dynamos only work in 3-D.
Fortunately, some interesting solutions can already be obtained at fairly
low resolution, for example of 163 meshpoints.
These flows have a α effect that can be determined either by
imposing an external magnetic field or by using the test-field method.
Direct simulations
→ Working material: helical-MHDturb/,
helical-MHDturb.tar.gz
[untar this file by typing tar zxf helical-MHDturb.tar.gz]
We begin with direct simulations showing dynamo action and the generation
of large-scale magnetic fields on the scale of the box for turbulent eddies
that are around 3 times smaller.
The late saturation behavior can be understood in terms of
magnetic helicity conservation.
As initial condition you may use either use a random field or
a Beltrami field, i.e.
&magnetic_init_pars
!initaa='Beltrami-y', amplaa=-0.01 !(+ve amplaa means now positive helicity)
initaa='gaussian-noise', amplaa=1e-4
/
We use a random forcing by invoking in run.in
&forcing_run_pars
iforce='helical', force=0.07, relhel=1.
/
Movie example for 163 meshpoints
Connection with mean-field theory
→ Additional working material: RobertsFlow/,
RobertsFlow.tar.gz
[untar this file by typing tar zxf RobertsFlow.tar.gz]
- Verify that by imposing a magnetic field in the x direction, you find
for Rm=2 (1/eta is called eta1 in run.in, and u=k=0) that α=-0.465.
(Look at uxbm in the output line.)
- In the absence of the imposed field, what is the critical value of Rm?
Change Rm such that the growth rate becomes marginal.
→ Additional working material: RobertsTestfield/,
RobertsTestfield.tar.gz
[untar this file by typing tar zxf RobertsTestfield.tar.gz]
- Using the test-field method with k=0 (in run.in this is means ktestfield=0)
check that for Rm=2 that α11=α22=-0.465.
- Now put k=1 (ktestfield=1) and show that
α11=α22=-0.299 and
η11=η22=0.188 and
Numerical Experiments homepage
$Date: 2012-03-18 17:42:51 $, $Author: brandenb $, $Revision: 1.4 $