LABORATOIRE CASSIOPÉE - O. C. A.

Séminaire

Phénomènes Physiques et Modèles Mathématiques en Sciences de l'Univers

Le séminaire a lieu le vendredi 2 décembre 2005 de 14h00 à 15h00
dans la salle de réunion du PHC (Observatoire de Nice). 

Multiscale MHD systems with a vanishing or non-significant alpha-effect

Vlad Zheligovsky

  International Institute of Earthquake Prediction theory and Mathematical geophysics, Moscow 

& Laboratory Of general Aerodynamics, Instute of Mechanics, Lomonosov Moscow State University

We consider linear and non-linear stability of short-scale MHD systems to
large-scale perturbations, where, usually due to appropriate symmetries,
alpha-effect is insignificant. The perturbation is expanded in the series
in the scale ratio. The standard multiscale techniques are used to derive
equations for large-scale mean-field components of the perturbation as the
solvability condition of the order 2 equations. No usual assumptions are
made, e.g. the basic short-scale MHD state is not required to be
space-periodic or steady. Furthermore, an account of the Coriolis force istaken, 
resulting in further algebraic difficulties.
In particular, the following systems are considered:
1) parity-invariant MHD system (the Navier-Stokes & magnetic induction equations) in the entire space;
2) a convective MHD system (the Navier-Stokes, magnetic induction and heat transfer equations), 
symmetric about a vertical axis, in a layer.