The process in which the anatomical structures of the descending aorta are generated and organized. The descending aorta is the portion of the aorta in a two-pass circulatory system from the arch of aorta to the point where it divides into the common iliac arteries. In a two-pass circulatory system blood passes twice through the heart to supply the body once. [ http://purl.obolibrary.org/obo/UBERON_0001514 http://www.informatics.jax.org/searches/AMA.cgi?id=MA:0002571 GOC:dgh http://en.wikipedia.org/wiki/Descending_aorta GOC:bf ]