IPP Annual Report 2007 - Max-Planck-Institut für Plasmaphysik ...

Max Planck Junior Research Group
“Turbulence in Magnetized Plasmas”
Head: Dr. Wolf-Christian Müller
Turbulent Convection
Turbulence driven by thermal fluctuations around a mean
temperature gradient plays a role in various physical systems
like the Sun, the earth’s atmosphere, and fusion plasmas.
Large scale direct numerical simulations of turbulent convection
in plasmas as well as neutral fluids described in the Boussinesq
approximation were performed using a parallel pseudospectral
code in fully periodic geometry. Two dimensional magnetohydrodynamic
(MHD) convective turbulence shows self-excited
quasi-oscillations between regimes that are either dominated by
buoyancy or by inertial forces depending on the mutual alignment
between velocity and magnetic field. In addition, a simulation of
a three-dimensional hydrodynamic system with 20483 collocation
points has been started, making this simulation the largest
numerical effort in turbulent convection world-wide. To this end,
the numerical code has been highly optimized for the HLRBII
supercomputer at the Leibniz computing centre in Garching.
Lagrangian Statistics of Turbulence
Turbulent transport is a key feature of many physical problems
such as plasma confinement in fusion devices, the turbulent
dynamo, or the propagation of cosmic rays in the interstellar
medium. The diffusive characteristics of turbulence are best
studied from the Lagrangian viewpoint. Lagrangian statistics
of incompressible magnetohydrodynamic turbulence are obtained
by tracking tracer particles in direct numerical simulations.
A full parallelization of the particle tracking scheme has
made it possible to use up to 1024 parallel processes. In MHD
turbulence under the influence of a mean magnetic field turbulent
diffusion and relative dispersion of the tracer particles
has been found to be enhanced in the direction of the mean
magnetic field. The results agree with the picture which has
been developed for macroscopically isotropic MHD turbulence.
Turbulent flows are commonly driven by temperature gradients.
Therefore, Lagrangian tracers have been added to the
large HLRBII-run of convective Navier-Stokes turbulence.
Compressible Turbulence
Within the Cluster of Excellence “Origin and Structure of the
Universe” the efforts to study supersonic turbulence focus on
turbulent dynamics which are probably of importance for starand
structure-formation in the interstellar medium. To this end,
a new numerical framework is being developed to work reliably
on turbulent configurations with Mach numbers greater than
five. Special attention is paid to a low dissipation approach since
thin and sharply resolved shock fronts are a dominant feature
of supersonic turbulence. The new 2D and 3D compressible
MHD codes are able to capture shocks while maintaining the
divergence free constraint on the magnetic field. The underlying
Theoretical Plasma Physics
89
numerical scheme of Kurganov-Tadmor type in combination
with third order CWENO reconstruction is built on central differences
meeting the requirements of low numerical dissipation and
of high precision. The code has been successfully tested for accuracy
and for its shock capturing ability and is currently being parallelized.
The project represents a direct point of contact with astrophysics
groups of the MPA (Hillebrandt) and LMU (Burkert).
Structure Formation in MHD Turbulence
Magnetic helicity quantifies various structural aspects of a
magnetic field. It is important in reversed-field-pinch experiments
as well as in astrophysical plasmas since its dynamics
is believed to be the cause of large scale magnetic structures
accompanying many celestial bodies. We study the associated
inverse cascade, i.e., the self-similar spectral transport from
small scales to large scales by means of direct numerical simulations
of 3D MHD turbulence. Systems with small scale drive
of turbulence and magnetic helicity have been set up resulting
in a clearly established cascade process whose characteristics
are in contradiction to all known theories. Current studies
focus on a more realistic representation of the small scale
dynamics of turbulence to verify this finding. In a complementary
activity, the behaviour of magnetic helicity in decaying
3D MHD turbulence is investigated numerically.
Fundamental Properties of Turbulence
The investigation of anisotropic cascade dynamics in MHD turbulence
permeated by a strong mean magnetic field is continued.
Recent numerical experiments as well as detailed diagnostics
of large scale simulations have led to serious doubts about the
validity of the well-accepted Goldreich-Sridhar picture of anisotropic
turbulence. Further efforts will be necessary to corroborate
this claim. Numerical investigations of the monoscaling property
of probability density functions (PDFs), recently found in the
solar wind, show that this feature is probably a new universal
symmetry of turbulence. We found it in various turbulent MHD
and Navier-Stokes systems for the two-point energy fluctuations.
The PDFs resemble Levy laws of gamma-type ~1/x 1+k exp(-x/x 0 ),
k>0. A newly developed theory in the spirit of polymer fragmentation
models explains the observed behaviour as a consequence
of a turbulent transfer process in spectral space and restricts the
monoscaling property to cascading quantities like energy or density
(in the compressible case). Triad interactions, the fundamental
building blocks of non-linear dynamics in incompressible turbulence,
are studied in 3D Navier-Stokes and MHD-turbulence. After
the necessary diagnostic tool has been developed and successfully
tested on the dual cascade of 2D hydrodynamic turbulence,
the analysis is currently being extended into the third dimension.
Scientific Staff
A. Busse, T. Hertkorn, S. Malapaka, M. Momeni, D. Škandera,
Y. Rammah, Ch. Vogel.