Abstract

Numerical Analysis of Finite-Amplitude Wide Acoustic Beams in Two-Phase Marine Sediments

N.S.Bakhvalov (Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia); J.I.Osypik, N.I.Pushkina, Ya.M.Zhileikin (Research Computing Center, Moscow State University, Moscow, Russia)

e-mail: Bakhvalo@mech.math.msu.su

Numerical investigation of nonlinear three-dimensional acoustic wave propagation is finding increasing application in various problems where complicated combination of nonlinear and diffraction processes makes an analytical study very difficult. In the present report the computational analysis is applied to study high-intensity acoustic beam propagation in two-phase water-filled marine sediments. The mathematical model is based on the use of conservation schemes for evolution differential equations and conservation schemes of gas dynamics. These methods proved very promising in many nonlinear acoustics problems [Bakhvalov N.S., Zhileikin Ya.M. , Zabolotskaya E.A. Nonlinear theory of sound beams. Am. Inst. Ph., N.Y., 1987]. In the present work an approximate nonlinear wave equation is derived to describe the evolution of intense three-dimensional acoustic beam where the steepening of the wave front and shock formation are accompanied by self-focusing or spreading of the beam. The derived evolutionary equation is analysed numerically for various marine sediment physical parameters.

Section : 1