## 2pPAb6. Dispersion relation influence on rise times of sonic boom propagation through turbulence.

### Session: Tuesday Afternoon, May 14

### Time: 2:30

**Author: Allan D. Pierce**

**Location: Boston Univ., Dept. of Aerosp. and Mech. Eng., 110 Cummington St., Boston, MA 02215**

**Abstract:**

Recent work suggests the ``average'' turbulence contribution to rise times
is accounted for by an extra term in the propagation equation, evolving from an
extra term in the dispersion relation k=((omega)/c)+F((omega)), where c is
spatially averaged, and, for mechanical turbulence, F((omega)) depends on
turbulent energy dissipation rate (epsilon) per unit fluid mass. Previous
analysis suggests that F((omega)) is -7.48 C[inf K]e[sup i(pi)/3](epsilon)[sup
2/3]c[sup -7/3](omega)[sup 1/3]. The extra term's influence is explored with a
pulse beginning with a stepfunction in pressure which enters a turbulent
atmosphere. After propagation through a distance x, the rise time becomes of
order of (epsilon)[sup 2]c[sup -7]x[sup 3]. This cubic growth is eventually
curbed by the nonlinear steepening effect; the above prediction is an upper
limit to the turbulence contribution. The discrepancy with the 1971 prediction
that the rise time scales as (epsilon)[sup 4/7]c[sup -19/7]x[sup 11/7] is
discussed, such being consistent with an (omega)[sup 7/11] term in the
dispersion relation. [Work supported by NASA--LRC.]

from ASA 131st Meeting, Indianapolis, May 1996