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

## 5aPA7. Determination of turbulent velocity correlations by the nonlinear
scattering of crossed ultrasonic beams.

**Murray S. Korman
James E. Parker, III
**

**
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*Dept. of Phys., USNA, Annapolis, MD 21402
*

*
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The nonlinear interaction of two, mutually perpendicular crossed
ultrasonic beams, overlapping in the presence of turbulence, generates a
scattered sum frequency component that radiates outside the interaction region.
In the absence of turbulence, virtually no scattered sum frequency component
exists (outside the interaction region). A theoretical investigation is
reported that relates the shape of the ensembled averaged scattered sum
frequency intensity spectrum, I[sub +] ((omega),(theta)[sub *]) (which exhibits
a Doppler shift, frequency broadening, skewness, and kurtosis), to the
scattering angle (theta)[sub *], incident and scattered wave vectors (where
K[sub +]=k[sub s]-[k[sub 1]+k[sub 2]]), and statistical properties of the
turbulent velocity field v. The n spectral moments <(K[sub +](centered
dot)v)[sup n]>(proportional to)(integral)I[sub +]((omega),(theta)[sub *])
((omega)-<(omega)>)[sup n] d(omega) (obtained from experiment) are used to
evaluate turbulent velocity correlations like , where n=2.
The scattering geometry involves rotating the axis of the transmitting crossed
beams (which are always perpendicular to each other) in the plane containing
the submerged circular water jet and receiver axes. Angle (theta)[sub *] is
measured between the ray bisecting the transmitting axes and the stationary
receiver axis. The crossed beams are focused and overlap at the common focal
point. Spectral moments, obtained from scanning the overlap region across the
jet, are used to predict velocity correlations across the width of the jet with
good spatial resolution.