Large-scale dynamos in turbulent convection with shear - Petri

Good introductory link to the Solar Dynamo: scholarpedia article

http://www.scholarpedia.org/article/Solar_dynamo


Related publication: http://arxiv.org/abs/0806.0375


Need shear to avoid catastrophic quenching. Dual role of shear: generation and helicity loss.

New Users

Andrej

Relative Velocities and Collision Speeds of Particles in PPDs

Voelk et al. (1980) -> long standing result for formulas for relative velocities of two particles with different stopping times.

Particles of different stopping times drift differently and meet at higher velocities. Growth is hindered away from the diagonal.

First Science: shearing boxes with the Pencil code, forced hydro turbulence, MRI.

Results of collisional speeds.

Martin

Magnetic field dissipation in a jet

Originally for Poynting-flux dominated flows. If the field decays faster than 1/r it produces acceleration even beyond the Alfven radius (The radius at which magnetic pressure equals the thermal pressure, nearly equal to the magnetospheric radius).

Naturally produces radiation (gyromagnetic, ciclotron, sincrotron)

MHD in expanding coordinates. Interplay jet/box. IC: steady state wind 1D (1.5D solution)

BC: the biggest possible in the radial direction... (?)


Raphael

Chemical Symmetry breaking. One of the processes that was quite important for the emergence of life. Applications to astrobiology (explains why there is a "astrobiology_data" subroutine in chemistry.f90)

Plan to use the Pencil code in this problem: Inhomogeneities in the energy source. Put some localized sources of energy. Chemicals coming from crust, or light coming from above.

Excitation of Inertial-Acoustic Waves in PPDisks (Tobi)

Properties of Keplerian flows that develop in the accretion disk. Shear, angular momentum transport, etc, check Balbus & Hawley 1998 for a thorough review.

Propagation of waves in the MRI turbulence. High-time resolution needed to see the waves. Some people have seen it before but mistook it as numerical artifacts.

The waves are trailing.

Radial wavenumber depends linearly in time. The fourier modes swing successively from leading (kx/ky<0)>0).

The power shows shear in k-space.

Inertial acoustic wave equation

d2p/dt2+[k^2c^2+Omega^2]p=-c^2 i kx(t) ksi + (q-2)Omega*Nx + dNy/dt

ksi=vortensity

N=div(T), T=stress tensor (nonlinear terms)

WBKJ analysis reveals that there is a preferred wavenumber for which the amplitude of the waves is maximum. The preferred wavenumber is very low.

The steady damping of the waves seen towards high wavenumbers may be due to turbulent diffusion.

A Monte-Carlo coagulation-fragmentation model for the Pencil Code (Andras)

Link to the talk (pdf)

Try overcoming the meter sized barrier by coagulation instead of self-gravity

1g -> 1e12 monomers inside a particle. Not feasible with current computers.

Need something more statistical.

Critics to Ander's nature paper: starts with particles that are already too big (40-60-80)cm, and without dust physics (coagulation-fragmentation; CF). Can planet formation work with smaller particles and detailed CF models?

Method. Add virtual particles. Real particles grow by colliding with virtual particles. Real particles do not meet, the rate of collision real-real is much smaller than real-virtual. The model is just real-virtual. There are no virtual-virtual collision either.

Test: Smoluchowski equation that describes coagulation. The test reproduces the mass x number density distribution. For comparison, see Ormel et al. 2008, Wetherill 1990.

Important energies: Eroll-> Energy needed to rotate a monomer by 90 degrees.

Porosity model:

Ecoll < 5Eroll (Hit and stick)

If 5Eroll < Ecoll < Efrag (compaction)

Fragmentation always lead to a monomer (limitation)

With porosity, the radius gets bigger by a factor 2 compared to just using turbulence + brownian
motion.

For the model showed, the grains reach complete compactness at 0.1cm size. The MMSN reaches compactness just at m size.

The code seems fast. 1 million timesteps takes minutes in a single processor. Seems no overhead for the pencil code.

Simulations of the geodynamo (Graeme)

Link to talk (pdf)

Thermal convection in a rotating spherical shell of weakly compressible fluid (motivated by geodynamo)

Cartesian domain (equivalent to lsphere_in_a_box)

Damping outside boundaries (for velocity and entropy)

Standard MHD with Laplacian diffusion (what's the Reynolds number?)

Polytropic ideal gas with a background state (density and temperature)

Non-equidistant grid outside the shell (step-linear)

Full sphere and half-sphere runs. Mag field boundaries: Btan=0, d(Bn)/dn=0. (Has to be adapted for spherical coordinates.)

Comparison with Kageyama & Sato, Phys Plasmsas, 1995 (KS95). Early results (McMillan and Sarson, PEPI, 2005) are not correct due to scaling glitch. (cp=1 and R=2/5 were hard-coded in the Pencil Code at that time, before the EquationOfState module was developed.)

Weak dependence of vorticity on the polar direction for non-magnetic convection.

When putting the magnetic field with small magnetic diffusivity (high Rm), dynamo action is obtained. At higher Rm, the simple convection roll pattern is disrupted.

There is a dynamo benchmark in the geodynamo community (Christensen et al., PEPI, 2001), but just for the Boussinesq case . Unfortunately this is not a stable state for a compressible gas.

Qualitatively speaking, the results are similar to another dynamo benchmark.

Future work:

• tidy up and publish (good plan)
• further investigate reversing solutions

• Boussinesq and anelastic fluids
• spherical coordinates
• insulating boundary conditions
• make Coriolis force implicit
  

• Local box simulations of geodynamo

Testfield method (Axel)

Links to the talk ( ppt, pdf)
Prolific output in 2008 after quiescent period after 2005

In many astrophysical systems a large scale magnetic field is generated, but the mechanism for their formation is still elusive.


Helical turbulence: Homogeneous and isotropic. However, all helices have the same handiness.


Large scale magnetic fields usually appear in spacetime plots of fields as a finite amplitude field after dimensional average.


Source of turbulence in forced dynamos: a body force. Non-natural, closest analog being supernova explosions.

Convection (with shear) and MRI are two sources of turbulence that can generate large magnetic fields. Structure visible in the z-direction.

Low Prandlt number dynamos (Pm=visc/resist):

Helical turbulence: inject energy at intermediate wavelengths. Energy cascades to the right (smaller wavelengths) and to the left (larger scales). This is due to helicity. At non-helical turbulence at other Pradtl numbers, one can excite the dynamos at progressively lower Reynolds numbers as the Prandlt number increases. In the Sun the Prandt number is 1e-5. So, very large Reynolds numbers are needed.

With helical turbulence the dynamo is still excited at low Prandlt numbers. The only difference is that the viscous range moves towards larger scales (still smaller than the scale where energy in being forcely supplied). The inertial range shrinks. So, astrophysics don't have any problems with small Prandlt numbers. The only thing we need is stratification to drive helicity loss.

Testfield equations:
perturb the original induction equation and separate them in mean field and fluctuations. The eq. for the fluctuations cannot induce a large scale field.

Validation: Roberts flow
Non-linear alpha and eta tensors
Turbulent diffusion as a function of Reynolds number. Quenching goes as a factor 5. Turbulent diffusion is not catastrophically quenched. Several consistency checks.

Turbulent Combustion (Natalia)

Link to the talk (pdf)

Outline of theory, challenges and preliminary results.

Many species, every single one of them contributes to the fluid equations.

The pressure is

P=m/mu * R * T

1/mu=Sum_k (Y_k/m_k)

And this now is a pencil.

Initial condition: air mixture at atmospheric pressure and high temperature (1200K)

Reaction mechanisms (8 equations) are used instead of the 19 of the Li mech Nils talked about. They should give the same results, but the code is not yet at that stage.