A nozzle arrangement for use with a supersonic jet engine configured to produce a plume of exhaust gases when the supersonic jet engine is operating at a predetermined power setting and moving at a predetermined Mach speed, the nozzle arrangement comprising: a nozzle configured to produce a plume of exhaust gases, the nozzle having a trailing edge oriented at a predetermined angle with respect to an axial direction of the nozzle; and a plug body partially positioned within the nozzle and coaxially aligned with the nozzle, the plug body having an expansion surface and a compression surface downstream of the expansion surface wherein the expansion surface is spaced apart from the trailing edge to define an outlet of the nozzle, a protruding portion of the plug body extending downstream of the trailing edge for a length greater than a conventional plug body length such that the protruding portion of plug body extends downstream further than an intersection point of Mach lines propagating off an internal surface of the trailing edge when the supersonic jet engine is operating at the predetermined power setting and moving at the predetermined Mach speed, wherein the plug body has a surface geometry configured to cause the plume of exhaust gases to have a static pressure that is substantially equal to a static pressure of a free stream of air flowing past the trailing edge, the protruding portion of the plug body having a substantially circular cross section along substantially an entire longitudinal length of the protruding portion of the plug body, the expansion surface configured to allow exhaust gases to expand in a direction away from the free stream and the plug body and protruding portion having a contour and configuration configured to shape the plume of exhaust gases such that the plume of exhaust gases flows substantially parallel to a direction of a free stream of air flowing off of the trailing edge of the nozzle proximate the trailing edge of the nozzle and the compression surface configured to return the exhaust gases to an axially aligned flow and the protruding portion having a contour and configuration further configured to cause the plume of exhaust gases to isentropically turn the free stream of air flowing off of the trailing edge of the nozzle at a location downstream of the trailing edge of the nozzle such that a free stream of air flowing off of the trailing edge moves in a direction parallel to a longitudinal axis of the plug body. a nozzle configured to produce a plume of exhaust gases, the nozzle having a trailing edge oriented at a predetermined angle with respect to an axial direction of the nozzle; and a plug body partially positioned within the nozzle and coaxially aligned with the nozzle, the plug body having an expansion surface and a compression surface downstream of the expansion surface wherein the expansion surface is spaced apart from the trailing edge to define an outlet of the nozzle, a protruding portion of the plug body extending downstream of the trailing edge for a length greater than a conventional plug body length such that the protruding portion of plug body extends downstream further than an intersection point of Mach lines propagating off an internal surface of the trailing edge when the supersonic jet engine is operating at the predetermined power setting and moving at the predetermined Mach speed, wherein the plug body has a surface geometry configured to cause the plume of exhaust gases to have a static pressure that is substantially equal to a static pressure of a free stream of air flowing past the trailing edge, the protruding portion of the plug body having a substantially circular cross section along substantially an entire longitudinal length of the protruding portion of the plug body, the expansion surface configured to allow exhaust gases to expand in a direction away from the free stream and the plug body and protruding portion having a contour and configuration configured to shape the plume of exhaust gases such that the plume of exhaust gases flows substantially parallel to a direction of a free stream of air flowing off of the trailing edge of the nozzle proximate the trailing edge of the nozzle and the compression surface configured to return the exhaust gases to an axially aligned flow and the protruding portion having a contour and configuration further configured to cause the plume of exhaust gases to isentropically turn the free stream of air flowing off of the trailing edge of the nozzle at a location downstream of the trailing edge of the nozzle such that a free stream of air flowing off of the trailing edge moves in a direction parallel to a longitudinal axis of the plug body.