Systematic construction of exact 2-D MHD equilibria with steady, compressible flow in Cartesian geometry and uniform gravity

¹ Department of Physics, University of Crete, PO Box 2208, 710 03 Heraklion, Crete, Greece
² Department of Astronomy & Astrophysics and Enrico Fermi Institute, University of Chicago, 5640 S. Ellis Ave., Chicago, IL 60637, USA e-mail: vlahakis@jets.uchicago.edu
³ Department of Physics, University of Crete, PO Box 2208, 710 03 Heraklion, Crete, Greece e-mail: tsingan@physics.uoc.gr

Corresponding author: G. J. D. Petrie, gordonp@physics.uoc.gr

Received: 14 September 2001
Accepted: 16 November 2001

Abstract

We present a systematic method for constructing two-dimensional magnetohydrodynamic equilibria with compressible flow in Cartesian geometry. This systematic method has already been developed in spherical geometry and applied in modelling solar and stellar winds and outflows (Vlahakis & Tsinganos [CITE]) but is derived here in Cartesian geometry in the context of the solar atmosphere for the first time. Using the method we find several new classes of solutions, some of which generalise known solutions, including the Kippenhahn & Schlüter ([CITE]) and Hood & Anzer ([CITE]) solar prominence models and the Tsinganos et al. ([CITE]) coronal loop model with flow, and some of which are completely new. Having developed the method in full and summarised the several classes of solutions, we explore in a some detail one of the classes to illustrate the general construction method. From one of the new classes of solutions we calculate two loop-like solutions, one of which is the first exact two-dimensional magnetohydrodynamic equilibrium with trans-Alfvénic flow.