### ASA 126th Meeting Denver 1993 October 4-8

## 5aPA4. Propagation of transient waves in a random medium.

**Alan R. Wenzel
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*NASA Langley Res. Ctr., MS 460, Hampton, VA 23681-0001
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A theoretical analysis of the propagation of transient scalar waves in a
one-dimensional random medium is presented. The index of refraction of the
medium is assumed to deviate only slightly from unity, which allows the
analysis to be carried out with the aid of a perturbation method. The specific
approach adopted here combines a renormalization technique with a
travel-time-corrected averaging procedure called asynchronous ensemble
averaging. A general expression, valid for an arbitrary initial disturbance, is
obtained for the variance of the wave. From that result, an expression for the
variance is derived for the special case in which the initial disturbance has
the form of a ramp function with arbitrary slope. These results show that the
variance of the wave is directly proportional to the variance of the refractive
index of the medium, but is only weakly dependent on the propagation path
length. It is also found that, as the slope of the ramp function decreases, the
wave variance decreases as well. The presentation concludes with some
observations on the relevance of these results to the problem of sonic-boom
propagation in the atmosphere. [Research supported by NASA.]