Nonlinear propagation of shaped supersonic signatures through turbulence

The amplitude and loudness of conventional N-wave sonic booms vary randomly after propagating through atmospheric turbulence towards the ground. Recent studies have shown that the turbulence effect depends on the amplitude of incoming N-wave. The next generation of supersonic aircraft are designed to produce shaped booms, which are generally lower in amplitude than N-waves and contain shocks with much longer rise times. In this paper, the effect of nonlinearity on shaped sonic booms propagating through turbulence is compared with that for N-waves. Results suggest that nonlinearity may have a negligible impact on loudness variations for shaped signatures, while the impact for N-waves can be significant. Propagation is modeled by solving an augmented KZK propagation equation including the effects of diffraction, thermoviscous absorption, relaxation, nonlinearity, and wind fluctuations.The amplitude and loudness of conventional N-wave sonic booms vary randomly after propagating through atmospheric turbulence towards the ground. Recent studies have shown that the turbulence effect depends on the amplitude of incoming N-wave. The next generation of supersonic aircraft are designed to produce shaped booms, which are generally lower in amplitude than N-waves and contain shocks with much longer rise times. In this paper, the effect of nonlinearity on shaped sonic booms propagating through turbulence is compared with that for N-waves. Results suggest that nonlinearity may have a negligible impact on loudness variations for shaped signatures, while the impact for N-waves can be significant. Propagation is modeled by solving an augmented KZK propagation equation including the effects of diffraction, thermoviscous absorption, relaxation, nonlinearity, and wind fluctuations.