The issue of noise generated from aircraft jet engine exhaust has become an important consideration for current and future engines. The ability to predict the acoustic characteristics of an exhaust depends on the accurate prediction of the nozzle plume and associated turbulence quantities using computational fluid dynamics (CFD) methods. There are a variety of exhaust system concepts being considered for noise reduction. Some of these concepts are complex and thus the question of the ability of CFD codes to accurately predict the plume characteristics arises. To address this question, a relatively simple axisymmetric, two stream nozzle plume that will provide a basis for evaluating the current state of the art in the prediction of nozzle plumes has been studied. The two streams simulate fan and core flows in a typical turbofan engine. Two CFD codes were applied to this problem to corroborate the computational results ahead of the tests. NPARC solves the full Navier-Stokes equations while the other code, PAB3D, solves the thin-layer Navier-Stokes equations. The comparison of the centerline velocities obtained from the two codes indicates a similar decay rate, although the NPARC results indicate a lag in the start of the centerline decay as compared to PAB3D. This difference may be due to the way the compressibility corrections were applied in the turbulence models. Overall, the jet plume characteristics predicted by the two codes show similar results.