Ruderman, M.S. and Brevdo, L. (2006) Stability of an MHD shear flow with a piecewise linear velocity profile. Astronomy and Astrophysics, 448 (3). pp. 11771184. ISSN 14320746

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Abstract
In this paper we present the results of the stability analysis of a simple shear flow of an incompressible fluid with a piecewise linear velocity profile in the presence of a magnetic field. In the flow, a finite transitional magneticfree layer with a linear velocity profile is sandwiched by two semiinfinite regions. One of these regions is magneticfree and the flow velocity in the region is constant. The other region is magnetic and the fluid in it is quiescent. The magnetic field is constant and parallel to the flow in the transitional layer. The fluid density is constant both in the magnetic as well as the magneticfree regions, while it has a jumptype discontinuity at the boundary between the transitional layer and the magnetic region. The effect of gravity is included in the model, and it is assumed that the lighter fluid is overlaying the heavier one, thus no RayleighTaylor instability is present. The dispersion equation governing the normalmode stability of the flow is derived and its properties are analysed. We study stability of two cases: (i) magneticfree flow in the presence of gravity, and (ii) magnetic flow without gravity. In the first case, the flow stability is controlled by the Rayleigh number, R. In the second case, the control parameter is the inverse squared Alfvénic Mach number, H . Stability of a particular monochromatic perturbation also depends on its dimensionless wavenumber α. We combine the analytical and numerical approaches to obtain the neutral stability curves in the (α,R)plane in the case of the magneticfree flow, and in the (α,H)plane in the case of the magnetic flow. The dependence of the instability increment on R in the first case, and on H in the second case is treated. We apply the results of the analysis to the stability of a strongly subsonic portion of the heliopause. Our main conclusion is as follows: The inclusion of a transitional layer near the heliopause into the model increases by an order of magnitude the strength of the interstellar magnetic field required to stabilize this portion of the heliopause in comparison with the corresponding stabilizing strength of the magnetic field required when modelling the heliopause as a tangential discontinuity.
Item Type:  Article 

Copyright, Publisher and Additional Information:  © ESO 2006. Reproduced with permission. 
Keywords:  magnetohydrodynamics (MHD),solar wind, instabilities, ISM, 
Institution:  The University of Sheffield 
Academic Units:  The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) 
Depositing User:  Repository Officer 
Date Deposited:  17 Nov 2006 
Last Modified:  05 Jun 2014 20:31 
Published Version:  http://dx.doi.org/10.1051/00046361:20053854 
Status:  Published 
Publisher:  EDP Sciences 
Refereed:  Yes 
Identification Number:  10.1051/00046361:20053854 
URI:  http://eprints.whiterose.ac.uk/id/eprint/1718 