EDP Sciences
Free access
Volume 413, Number 1, January I 2004
Page(s) 7 - 15
Section Cosmology
DOI http://dx.doi.org/10.1051/0004-6361:20031536

A&A 413, 7-15 (2004)
DOI: 10.1051/0004-6361:20031536

Absolute and convective instabilities in open shear layers

II. Magnetohydrodynamic equilibrium
M. Terra-Homem and R. Erdélyi

Space and Atmosphere Research Centre, Dept. of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
    e-mail: m.homem@sheffield.ac.uk; robertus@sheffield.ac.uk
(Received 4 April 2003 / Accepted 18 September 2003)

The present paper is the continuation of our study of absolute and convective instabilities in open shear layers (Terra-Homem & Erd´elyi 2003). In this paper the effects of a magnetic field are included and a series of fully non-linear ideal polytropic 2D MHD numerical simulations is carried out. The amount of mean flow required to sweep away the perturbation before it grows and destroys the whole flow is calculated for various configurations of the magnetic field. The analytical results obtained by Fej´er (1964) for a velocity discontinuity were recovered with a very good accuracy. The study focused on uniform, discontinuous and sheared magnetic fields. We found that the value of mean flow needed for a perturbation to become convectively unstable (critical mean flow) decreased with decreasing value of the plasma  $\beta$. We also found that the low $\beta$ value side, of a discontinuous and sheared magnetic field, is predominant in the behaviour of the instability. Finally we show the thickness of the magnetic shear layer has no effect on the value of critical mean flow.

Key words: magnetohydrodynamics (MHD) -- instabilities

Offprint request: R. Erdélyi, robertus@sheffield.ac.uk

© ESO 2004