  Magnetohydrodynamic configurations with strong localized current
concentrations and vortices play an important role for 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 Alfven-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 2D it is possible
to have current but no vortex sheets. In 2D vortex sheets of field
aligned-flows can also exist without strong current sheets, taking the limit of
small Alfven Mach numbers into account. The current sheet can vanish if the
Alfven 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 Alfven 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.
