### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 5pPAb7. Nonlinear acoustics of bubbly liquids: Traveling waves in a
quadratic approximation.

**Daniel Goldman
**

**
Ali Nadim
**

**
Paul E. Barbone
**

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

*
*
An important aspect of underwater acoustics is the effect of trapped
clouds of air bubbles. Recently, an approach to wave propagation in dilute
bubbly liquids was described in which the Rayleigh--Plesset equation is used to
derive a nonlinear equation of state for the gas bubble-liquid mixture [Nadim
et al., Bull. Am. Phys. Soc. 39, 1976 (1994)]. In this formulation, the
pressure in the mixture depends in a highly nonlinear way on the local density
and its first and second time derivatives. Linearization leads to the standard
acoustic equation for bubbly liquids. Here the quadratic approximation to the
nonlinear equation of state is examined, along with the related nonlinear wave
equation. The high- and low-frequency limits are then analyzed, and traveling
wave solutions are sought in each case. Comparison is made with existing
results for nonlinear waves in bubbly media.