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.
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