Statistics
Scientific paper
Dec 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004sf2a.conf...91b&link_type=abstract
SF2A-2004: Semaine de l'Astrophysique Francaise, meeting held in Paris, France, June 14-18, 2004. Edited by F. Combes, D. Barret
Statistics
Scientific paper
Because of the wide range of scales involved in MHD turbulence, a statistical approach may become necessary to keep a global view of this complex phenomenon. In particular, in the framework of the heating of the solar corona, the smallest events are not directly detectable by the current instruments but may be integrated to a statistical study. From the numerical point of view, the contradictory needs for computing speed and good description of MHD solutions may be addressed by simplified models, which keep the most possible of the complex and non-linear physics of the MHD equations but run sufficiently fast to produce statistics of fields, of structures, and of "events". We propose two such models which have been originally developed to represent coronal loops (with forcing and Alfvén wave reflection at the loop's foot-points), but which may be adapted to represent any region with a dominant large-scale magnetic field. The first model consists of a set of cellular automata, in which the non-linear terms of the MHD equations are modelled by a threshold dynamics on current density (Buchlin et al. A&A, 2003). In the second model, the cellular automata are replaced by shell-models of MHD, so as to reach a greater range of wavenumbers and to model more realistically the non-linear couplings between modes at different scales. The results obtained with these models will be presented and consequences of this study for observational statistics and for theory of MHD turbulence will be discussed.
Buchlin Eric
Galtier Sebastien
Velli M. M.
Vial Jean-Claude
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