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

## 1aPA2. The nonlinear interaction of two plane waves in a viscous medium.

**Zhong-Yue Jiang
**

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James F. Greenleaf
**

**
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*Biodynam. Res. Unit, Dept. of Physiol. and Biophys., Mayo Clinic and
Foundation, Rochester, MN 55905
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*
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Earlier studies [P. J. Westervelt, J. Acoust. Soc. Am. 29, 199--203,
934--935 (1957)] of the mutual nonlinear interaction of two plane waves of sound
with each other are extended to include the viscous effect. The viscous effect
is considered both from the equations of motion and the equation of state of the
medium. An analytical solution to the lowest order scattering process is
obtained if the viscous effect of second order and higher can be neglected. In
fact, it is shown that the scattered density (rho)[inf s] of two interacting
plane waves having the frequencies (omega)[inf 1] and (omega)[inf
2],respectively, satisfies the following equation: (open square)[inf v][sup
2](rho)[inf s]=(open square)[inf v][sup 2]{c[inf 0][sup -2]E[inf
12]+[(2cos(theta) +B/A)/2(omega)[inf 1](omega)[inf 2] (1-cos(theta))](del)[sup
2]W[inf 12] +[DB(c[inf 0][sup 2](omega)[inf 1](omega)[inf 2])[sup -1] /
4Ax(1-cos(theta))[sup 2]](del)[sup 2]((cursive beta)W[inf 12]/(cursive
beta)t)+[DB(3+cos(theta))/2Ac[inf 0][sup 4](1-cos(theta))]((cursive beta)V[inf
12]/(cursive beta)t)}, where E[inf 12], V[inf 12], and W[inf 12] are,
respectively, the total, potential, and special defined energy densities, D is
the sound diffusivity, B and A are nonlinearity parameters, (theta) is the
intersecting angle, and (open square)[inf v][sup 2] is a modified d'Alembertian
operator. [Work supported by CA43920 NIH.]