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We present a systematic method for constructing two-dimensionalmagnetohydrodynamic equilibria with compressible flow in Cartesian geometry.This systematic method has already been developed in spherical geometry andapplied in modelling solar and stellar winds and outflows (Vlahakis &Tsinganos,1998) but is derived here in Cartesian geometry in the context of thesolar atmosphere for the first time. Using the method we find several newclasses of solutions, some of which generalise known solutions, including theKippenhahn & Schl\"uter (1957) and Hood & Anzer (1990) solar prominence modelsand the Tsinganos, Surlantzis & Priest (1993) coronal loop model with flow, andsome of which are completely new. Having developed the method in full andsummarised the several classes of solutions, we explore in a some detail one ofthe classes to illustrate the general construction method. From one of the newclasses of solutions we calculate two loop-like solutions, one of which is thefirst exact two-dimensional magnetohydrodynamic equilibrium withtrans-Alfv\'enic flow.Comment: 12 pages, 12 Postscript figures, accepted by A&A 16th November 2001,  uses aa.cl

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