Abstract: It is known experimentally that a jet in forward flight radiates less noise than the same jet in a static environment. At a forward flight Mach number of 0.2, the noise reduction, depending on the jet operating conditions, could be as large as 4-5 dB in the sideline directions. In the past, a way to predict flight effects was to use the method of relative velocity exponent. Another method was to extrapolate measured static jet noise to the flight condition by means of scaling formulas. Both methods are semi-empirical. The fine scale turbulence jet mixing noise theory of Tam and Auriault (AIAA Journal, Vol. 37, No.2, pp. 145-153, 1999) is extended for applications to jets in forward flight. The effect of forward flight on the sources of fine scale turbulent jet mixing noise is also investigated. The noise from the fine scale turbulence of high speed nonaxisymmetric jets is considered. A prediction method is developed by extending the work of Tam and Auriault. A set of improved numerical boundary conditions for use in nonaxisymmetric jet mean flow and turbulence calculations is developed. It is known that nonaxisymmetric mean flow has a significant impact on the radiated noise spectrum and directivity through refraction. In the Tam and Auriault theory, this effect is accounted for by means of the adjoint Green's function. Here the adjoint Green's function method is extended to nonaxisymmetric flows. Extensive comparisons between calculated and experimentally measured jet noise spectra are presented. Good agreements are found. The noise from a jet installed under a wing of an aircraft is considered. A computational model for prediction of the radiated noise of the installed jet is developed. The parabolized Reynolds Averaged Navier-Stokes (RANS) equations supplemented by the k-epsilon model developed by Thies and Tam (AIAA Journal, Vol. 34, No.2, pp. 309-316, 1996) are modified and reformulated to compute the installed jet turbulent jet flow. The adjoint Green's function approach is extended to installed jets to include the flow effect and reflection from the wing.