Relation between current sheets and vortex sheets in stationary incompressible MHD

Abstract

Magnetohydrodynamic configurations with strong localized current concentrations and vortices play an important role in the dissipation of energy in space and astrophysical plasma. Within this work we investigate the relation between current sheets and vortex sheets in incompressible, stationary equilibria. For this approach it is helpful that the similar mathematical structure of magnetohydrostatics and stationary incompressible hydrodynamics allows us to transform static equilibria into stationary ones. The main control function for such a transformation is the profile of the Alfv́en-Mach number M A, which is always constant along magnetic field lines, but can change from one field line to another. In the case of a global constant M A vortices and electric current concentrations are parallel. More interesting is the nonlinear case, where M A varies perpendicular to the field lines. This is a typical situation at boundary layers like the magnetopause, heliopause, the solar wind flowing around helmet streamers and at the boundary of solar coronal holes. The corresponding current and vortex sheets show in some cases also an alignment, but not in every case. For special density distributions in 2-D, it is possible to have current but no vortex sheets. In 2-D, vortex sheets of field aligned-flows can also exist without strong current sheets, taking the limit of small Alfv́en Mach numbers into account. The current sheet can vanish if the Alfv́en Mach number is (almost) constant and the density gradient is large across some boundary layer. It should be emphasized that the used theory is not only valid for small Alfv́en Mach numbers M A≪1, but also for M A ≲1. Connection to other theoretical approaches and observations and physical effects in space plasmas are presented. Differences in the various aspects of theoretical investigations of current sheets and vortex sheets are given. © 2012 Author(s) CC Attribution 3.0 License.