Nonlinear wave propagation from a discrete annular array: Theory

Abstract

Theoretical investigations of finite amplitude wave propagation from bounded beam sources has been considered by Lee and Hamilton [J. Acoust. Soc. Am. 97, 906–917 (1995)] as well as others. These researchers have restricted their analyses to a source geometry of either an unfocused circular piston or a weakly, spherically focused circular piston. When the peak pressure does not exceed approximately 150 MPa, the Khokhlov–Zabolotskaya–Kuznetsov (KZK) nonlinear parabolic wave equation yields numerical solutions in agreement with experiments. However, little research has been reported on finite amplitude wave propagation from an array of discrete sources. Time domain simulations, based on the KZK equation, will be discussed for an eight element discrete annular array immersed in fresh and sea water. The source signal is typically a short sine wave tone burst with a center frequency of 500 kHz. The transitions from linear acoustics to nonlinear acoustics will be discussed, and comparisons between a spherically focused circular source and a properly phased array will be presented. While some data from recent experiments may be shown, the scope of this talk will be restricted to the theoretical treatment and the numerical simulations for the discrete annular array. [Work supported by ONR.] by Edson