Reduced 2D MHD Turbulence
Self-Organized Critical Cellular Automaton Model
Generalized Statistical Flare Model
Results of something as complex as a numerical simulation, should be viewed using any available way. Visualization in the form of a movie is always an efficient way of both understanding deeper the behavior of the simulated system and propagating better the applied ideas. A picture deserves more than a thousand words! Now, imagine this picture moving around! Have fun...
Reduced 2D MHD Turbulence
Self-Organized Critical Cellular Automaton Model
Generalized Statistical Flare Model
To investigate the
behavior as well as the spatiotemporal evolution of a
two-dimensional section of a magnetic loop
in the solar corona, we
have performed a numerical simulation whose evolution rules rely on
the theory of Turbulent Magnetohydrodynamics. In fact, we create a
Two-Dimensional Slab Geometry applying the reduced
2D MHD Equations.
For more detailed information, see
Georgoulis, Velli & Einaudi
(1998).
The movie has been constructed to illustrate the evolution of the current density in the grid over a limited period of time (100 simulation timesteps or ~ 2.7 h of real coronal time). Grid Resolution is 256x256 grid points. Bright features corresponds to areas of a high current density. In a two-dimensional configuration, these elongated structures are known as current sheets which are canceled by means of magnetic reconnection. In fact, you will notice quite a few current sheet disrupting during the movie performance. The movie is in MPEG format (~628 kB) Click on the image below.
The Statistical Flare is a
Three-Dimensional Cellular Automaton Model employed to reproduce the
spatiotemporal evolution of complex active regions in the solar
corona and to describe the system's long-term statistical behavior.
The model relies on the concept of Self-Organized
Criticality.
Instabilities occur with respect to a pre-defined critical threshold
and they may evolve in an avalanche-type manner. Further
information
is available in
Georgoulis & Vlahos,
(1996,1998).
The movie below illustrates the evolution in the three-dimensional box for a limited part of the timeseries (2000 simulation timesteps). Grid dimensions are 120x120x60. The clusters of points that blink on the screen are the spatial locations of various energy-release sites. A spatially connected collection of these points is what we call an avalanche. Along with the three-dimensional box, you can see a two-dimensional image which corresponds to the projection of the evolution on the base plane. The movie is in MPEG format (~3.14 MB) Click on the image below.
A generalization of the Statistical Flare. The
distinguishing features compared with the version given above are
the following:
In the above-described version, only one lattice site is
randomly selected, at the beginning of each iteration, to receive a
perturbation that could possibly trigger an instability. In this
version, a variable, larger than one, number of points, are
perturbed in each iteration. Therefore, we may record the
evolution of multiple
instabilities occurring simultaneously everywhere in the box. We
call this a Multiple Statistical Flare Model, in
distinction
with the previous Single Statistical Flare Model.
The initial configuration of the
model, which used to be completely random, is now organized in
loops.
We have assumed a
center-aligned, large-scale current
along
the magnetic polarity reversal line. This current flows on
the bottom plane of the box, giving rise to a dominant loop
orientation. The one footprint of a loop is located within the one
half of the bottom plane with its counterpart located on the other
half (we have also allowed, with a low probability, a number of
loops to have both footprints on the same half of the
bottom plane). Furthermore, we assume that if a loop, or a number of
loops, penetrate an energy release volume (like the ones you see on
the image above), then the entire loop becomes luminous
instantaneously. This assumption is compatible with an infinite
conductivity along the loop. A loop appears bright for as much time
as the duration of the energy-release event, given the fact that it
still penetrates the energy-release volume. The spatial propagation
of an event may switch on other neighboring loops. We do not take
into account two aspects of the real system, namely (a) the
finite conductivity along the loop which would give rise to a
gradual loop brightening and (b) the cooling time of the
plasma which could maintain the loop hot and luminous for some time
after the energy release process has fainted out. What you will see
now relates only to the heating timescale. We though underline our
desire to update this page with visualizations of more realistic
simulations, free of the above compromises.
The movie below illustrates a limited part of the simulated timeseries, namely 1930 simulation timesteps. Grid dimensions are 100x100x100. The movie is in MPEG format (it may take some time though; ~11.6 MB) Click on the image below.
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Page last updated on June 10, 2000
