On the relation of limiting characteristics to critical surfaces in magnetohydrodynamic flows

Details On the relation of limiting characteristics to critical surfaces in magnetohydrodynamic flows On the relation of limiting characteristics to critical surfaces in magnetohydrodynamic flows

Dec 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996mnras.283..811t&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 283, Issue 3, pp. 811-820.

Astronomy and Astrophysics

Astronomy

35

Mhd, Plasmas, Sun: Atmosphere, Solar Wind, Stars: Mass-Loss, Ism: Jets And Outflows

Scientific paper

We investigate the relation between critical surfaces and limiting characteristics or separatrices in the set of magnetohydrodynamic (MHD) differential equations that govern astrophysical flows such as winds, jets, accretion-type inflows, siphon flows in coronal loops, etc. For the particular case of axisymmetric self-similar solutions, we show that, at these critical/separatrix surfaces, the component of the flow velocity that is perpendicular to the directions of axisymmetry and self-similarity equals the slow/fast MHD wave speed in that direction. Our general analysis and claims are fully supported by analytical examples of three broad classes of axisymmetric self-similar solutions for flows in a uniform or spherical gravitational field. For these examples of exact solutions, we plot the various families of characteristics of the MHD partial differential equations. We then find that one member of each family of characteristics is asymptotically tangent to the corresponding separatrix which coincides with a critical surface there. Besides the well-known polytropic cases with constant polytropic index, more general flows with a variable polytropic index are also analysed.

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