Compressible 2D MHD modelling of prominence dips
  An analytical MHD model of a normal-polarity prominence with compressible flow is presented. The exact solution is constructed via a systematic nonlinear separation of variables method used to calculate several classes of MHD equilibria in Cartesian geometry and uniform gravity. Although the model is 2D, a third magnetic/velocity vector field component is included and the highly sheared fields observed in prominences are reproduced. A description is given of the balance of gas pressure gradient with gravity and the Lorentz or inertial forces acting along and across the prominence. It is found that the flow does not significantly influence the heating profile. The analyzed model has dimensions, plasma density, temperature and velocity profiles which agree with those in the observations literature. 
G.J.D. Petrie, K. Tsinganos & T. Neukirch