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Sonic booms are often modeled using Burgers equations accounting for dominant propagation effects. Scattering effects of turbulence, however, have not been incorporated into such equations, although these effects are ubiquitous in measured sonic booms. This paper formulates the mean scattering effects, including backscattering, using multiple scattering theory and ensemble averaging. It obtains an acousto-turbulence interaction energy representing the interaction of an acoustic wave�field with a turbulence �field. The interaction energy gives rise to a scattering wavenumber, a complex-valued correction to the free-space wavenumber. The scattering wavenumber leads to a dispersion and attenuation of the mean waveform due to backscattering, and can be obtained from a derived exact solution. An existing Burgers equation is extended to include the scattering effects of turbulence as an additional linear term. Numerical simulations of an N-wave and a low boom show that the mean scattering effects lead to shock thickening in the mean waveforms as well as reduce the peak amplitudes and total energy contents. The energy reduction is less severe in the low boom than in the N-wave and is dependent on the variance, correlation length, and thickness of the turbulence �field.

This paper reviews jet noise research conducted at the National Aeronautics and Space Administration (NASA) from the early 1950s to the present day. Research conducted by NASA’s predecessor, the National Advisory Committee for Aeronautics (NACA), and early years of NASA focused on turbojet noise, where a common approach for reducing jet noise was to limit the jet exit velocity to speeds that provided acceptable noise levels. Suppressors tested during this time resulted in thrust losses that were too severe to be implemented. With the introduction of turbofan engines in the 1960s, NASA shifted research to programs for both subsonic and supersonic aircraft applications with specific noise reduction goals. Subsonic research focused on increasing the bypass ratio of the engine to reduce the jet exit velocity of the core exhaust and adding mixers to the dual exhaust streams. Advances in computational methods improved aerodynamic designs and jet noise prediction tools. Supersonic applications proved to be more troublesome as programs aimed at large commercial transports required higher specific thrust engines. Changing the engine cycle to reduce jet noise was not compatible with mission range and speed requirements. Research for supersonic commercial aircraft remains an area of interest today at NASA.