ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

3aPAb5. Omega-to-the-one-third term in dispersion relation for acoustic pulse propagation through turbulence.

Allan D. Pierce

Boston Univ., Dept. of Aerospace and Mech. Eng., 110 Cummington St., Boston, MA 02215

The author's earlier formulation of pulse propagation through turbulence required a somewhat ad hoc separation of the effects of large scale and small scale turbulence with the selection of a cut-off turbulent wave number k[inf c] that separates the two regimes. A neater-cleaner formulation proceeds with the premise that the frequency dispersion of pulses is caused by that part of the turbulence spectrum which lies in the inertial range originally predicted by Kolmogoroff. The acoustic propagating wave's dispersion relation has the acoustic wave number being of the form k=((omega)/c)+F((omega)), where c is a spatially averaged sound speed and where, for mechanical turbulence, the extra term F((omega)) must depend on only the angular frequency (omega), the sound speed c, and the turbulent energy dissipation (epsilon) per unit fluid mass and per unit time. If the turbulence is weak, then the quantity F((omega)) has to be of second order in the portions of the turbulent fluid velocity in the intertial range, so, following Kolmogoroff's reasoning, it must vary with (epsilon) as (epsilon)[sup 2/3]. Simple dimensional analysis then reveals that F((omega)) is K(epsilon)[sup 2/3]c[sup -7/3](omega)[sup 1/3], the latter factor being as announced in the title of this abstract, and K being a universal dimensionless complex constant. A similar result holds for thermal turbulence. The analysis showing that the separating-out of the effects of turbulence in the inertial regime is in fact possible yields K=-0.37e[sup i(pi)/3]. The dispersion is typically small, but has an accumulative effect that leads to a sizable pulse distortion over large propagation distances. [Work supported by NASA Langley Research Center.]