The transversus' main function is to produce abdominal pressure in order to constrict the abdominal cavity and pull the diaphragm upward.

http://en.wikipedia.org/wiki/Pelvis

Lateral rotation (rotating either the trunk or the pelvis sideways) is achieved by contracting the internal oblique on one side and the external oblique on the other. The transversus' main function is to produce abdominal pressure in order to constrict the abdominal cavity and pull the diaphragm upward.