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.