A nozzle arrangement is disclosed herein for use with a supersonic jet engine that is configured to produce a plume of exhaust gases. The nozzle arrangement includes, but is not limited to, a nozzle having a trailing edge and a plug body partially positioned within the nozzle. The plug body has an expansion surface and a compression surface downstream of the expansion surface. A protruding portion of the plug body extends downstream of the trailing edge for a length greater than a conventional plug body length. The plug body is configured to shape the exhaust gases to flow substantially parallel to a free stream of air flowing off of the trailing edge of the nozzle and to cause the plume of exhaust gases to isentropically turn the free stream of air to move in a direction parallel to a longitudinal axis of the plug body.