A catharsis is a form of purgation that leaves a person feeling purified or renewed. Most often, the term is used to describe emotional purification. It can occur through direct emotional expression or by a significant subjective experience.
Given that many definitions use a form of the word purging to describe catharsis, an understanding of catharsis from the perspective of a person who purges food is warranted. For example, a person with bulimia nervosa will often feel an enormous urge to vomit after a binge; there is an intense feeling that the food will cause negative consequences if allowed to digest. When the purge is done, this powerful emotion does feel soothed. This is the essence of the notion of catharsis.
However, one could argue whether purging is an effective mode of catharsis in bulimia, because the effect often doesn't last long. The behavior of binging and purging is often repetitive. Worse, it generally leaves a person feeling worse because of guilt and shame. My opinion: It seems that a thoroughly cleansing emotional catharsis for a person with bulimia would be something that relieves the underlying emotions that drive the cyclical behavior.

