Macro-Sonix, 1054 Technol. Park Dr., Glen Allen, VA 23060
Ecole Centrale de Lyon, 69131 Ecully Cedex, France
Reported here is a numerical investigation to explain experimental observations of the effect of turbulence on N wave propagation [B. Lipkens, Ph.D. thesis, Mech. Eng. Dept., Univ. of Texas at Austin (1993)]. An adaptation of Von Karman's spectral model for incompressible, isotropic turbulence is used to generate a statistical realization of a turbulent field. The 2-D, random, isotropic velocity or temperature fields consist of a collection of discrete Fourier velocity modes [Ph. Blanc-Benon et al., Theoret. Comput. Fluid Dynamics 2, 271--278 (1991)]. The nonlinear propagation model consists of two parts: (1) Linear geometric acoustics is used to trace rays through each realization of the turbulent field, and (2) a nonlinear transport equation is derived for the propagation along the eigenrays and solved by a Pestorius-type algorithm. The input waveform to the algorithm is a plane N wave similar to that used in the model experiment to simulate sonic boom propagation through a turbulent atmosphere. Statistics of peak pressure and rise time, parameters that determine the loudness of sonic booms, are calculated over 100 realizations. The effect of turbulence is to reduce the nonlinear distortion of the N wave. On average, turbulence reduces peak pressure and increases rise time. Qualitatively, the same conclusions are observed as in the model experiment.