### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 3aPAa3. Weakly nonlinear propagation of N waves through turbulence.

**Bart Lipkens
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*Macro-Sonix, 1054 Technol. Park Dr., Glen Allen, VA 23060
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**Philippe Blanc-Benon
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*Ecole Centrale de Lyon, 69131 Ecully Cedex, France
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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.