Self-consistent three-dimensional steady state solutions of the MHD equations with field-aligned incompressible flow

We present self-consistent steady state solutions of the three-dimensional MHD equations including field-aligned incompressible flow. The solutions are calculated by a transformation method which allows the construction of steady state MHD solutions with subalfvénic flow from known solutions of static MHD and of steady state MHD solutions with superalfvénic flow from known solutions of steady state hydrodynamics. For the first time this transformation method is used to calculate self-consistent three-dimensional solutions of the steady state MHD equations with flow. We discuss possible applications of particular solutions to flow phenomena in the solar atmosphere such as the Evershed flow in sunspots and flows in coronal arcades.