The effects of a kinematic field of velocity fluctuations on the loudness metrics of two waveforms are examined with a three-dimensional one-way propagation solver. The waveforms consist of an N-wave and a simulated low-boom from NASA's X-59 QueSST aircraft. The kinematic turbulence is generated using a von Kármán composite spectrum, which is dependent on a root mean square (rms) velocity and outer scale of the turbulence. A length scale is proposed to account for the effect of the rms velocity and integral scale on the focusing and defocusing of the sonic boom waveform. The probability density function of the location of the first caustic attains a maximum value when the propagation distance is equal to the proposed length scale. Simulation results indicate that for small values of the nondimensional propagation distance, the standard deviation of the loudness metrics increases linearly. The loudness metrics follow a normal distribution within a given range of the nondimensional propagation distance. Results indicate the potential to parameterize the loudness metric distributions by the rms velocity and integral length scale.

Atmospheric boundary layer (ABL) turbulence causes variability of the sonic boom waveform at the ground. Recent numerical investigations of sonic boom propagation through kinematic velocity fluctuations indicate that loudness metric distributions are positively skewed relative to a normal distribution. This skewness depends on the propagation distance and turbulence intensity. Propagation simulations of N-waves and shaped booms through inhomogeneous ABL turbulence are presented. Meteorological conditions are varied to examine different daytime ABL conditions and their effect on sonic boom loudness distributions. Two outcomes are observed: (1) the loudness metric distributions become increasingly positively skewed as the propagation distance through the ABL increases, and (2) the distributions become increasingly positively skewed at the same lateral distance from the flight path as the convection level of the daytime ABL is increased. Thus, results indicate that ground level measurements of sonic boom loudness from flight tests performed at large lateral distances from the flight path may not be normally distributed, due to turbulence present in the ABL. (This research is supported by the Commercial Supersonic Technology Project of the National Aeronautics and Space Administration under Grant No. 80NSSC19K1685.)

Acoustic propagation in the atmosphere near the Earth’s surface at grazing incidence is influenced by ground impedance. Consequently, numerical simulations must use an impedance ground boundary condition in order to accurately predict ground effects associated with grazing incidence. A mixed Fourier transform method for impedance boundary conditions has been developed for parabolic approaches by the electromagnetics community. Here, the mixed Fourier transform method is adapted and validated for acoustic wave propagation. The one-way solution of the Helmholtz equation is computed with a modified angular spectrum approach to account for a locally reacting surface using a mixed Fourier transform in the vertical direction. Numerical simulations are presented that focus on sonic boom propagation near the ground in the shadow zone. The simulations demonstrate the utility of the mixed Fourier transform method to account for ground impedance effects that are ignored by ray theory-based propagation codes. Consequently, the method extends sonic boom prediction to the lateral cutoff and shadow zone regions. [This research is supported by the Commercial Supersonic Technology Project of the National Aeronautics and Space Administration under Grant No. 80NSSC19K1685.]

Recent flight tests during the Quiet Supersonic Flights 2018 (QSF18) study reported sonic booms heard outside of the primary carpet region. In the absence of turbulence, the lateral cutoff region separates the primary sonic boom carpet from the shadow zone, where the sonic boom signal experiences significant attenuation. However, when turbulence is present in the atmospheric boundary layer (ABL), additional scattering of the sonic boom to the shadow zone region occurs. A method is presented for simulating sonic boom propagation in a turbulent atmospheric boundary layer beyond the lateral cutoff region into the shadow zone. A split-step method is used to integrate a partially one-way equation for the acoustic pressure. Inhomogeneous turbulence, representative of the ABL, is generated in the computational domain with a Fourier synthesis approach. Distributions of several loudness metrics in the shadow zone region for a sonic boom N-wave and a shaped boom are examined. Increasing both turbulence root-mean-square velocity and integral length scale are found to increase the average loudness of booms in the shadow zone. (This research is supported by the Commercial Supersonic Technology Project of the National Aeronautics and Space Administration under Grant No. 80NSSC19K1685.)

Nonlinear acoustic propagation of sonic booms in the atmospheric boundary layer is considered in the context of a one-way solution to a third order wave equation. A split-step approach is utilized to compute different physical effects efficiently. Unlike previous approaches, the diffraction effects are computed exactly in the forward direction with no restriction on the angle of propagation. This results in more accurate modelling of sonic boom near the carpet edge. Heterogenous flow effects are incorporated with a wide-angle parabolic approximation. Nonlinear propagation is computed with a Burgers-Hayes method. Turbulence in the medium is constructed by the method of random Fourier modes. The turbulence spectra are constructed using an altitude dependent 3-dimensional von Karman spectrum. The turbulence field is considered frozen, as the eddy turnover time in the atmospheric boundary layer is generally much larger than the propagation time of the acoustic wave. Comparisons with benchmark predictions from the PCBoom software are conducted. The benchmark cases provide insight into the accuracy of the current prediction code for non-turbulent atmospheres. Future work is discussed regarding the prediction of shaped booms, boundary conditions, and predictions near the lateral extent of the boom carpet where previous approaches fail to capture the diffraction effects.