Journal of Computational Acoustics

One-dimensional traveling wave solutions to the fully nonlinear continuity and Euler equations in a bubbly liquid are considered. The elimination of velocity from the two equations leaves a single nonlinear algebraic relation between the pressure and density profiles in the mixture. On assuming the bubbles to have identical size and taking the volume fraction of bubbles in the medium to be small, an equation of state which relates the mixture pressure to the density and its first two material time-derivatives is derived. When this equation of state is linearized and combined with the laws of conservation of mass and momentum, a nonlinear, second-order, ordinary differential equation is obtained for the density as a function of the single traveling wave coordinate. A phase-plane analysis of this equation reveals the existence of two fixed points, one of which is a saddle and the other a node. A single trajectory connects the two fixed points and corresponds to a traveling shock wave solution when the Mach number of the wave, defined as the ratio of traveling wave speed to the low-frequency speed of sound in the bubbly liquid, exceeds unity. The analysis provides a qualitative explanation of the oscillations behind shocks seen in experiments on bubbly liquids.

We consider the Helmholtz equation in an axisymmetric cylindrical waveguide consisting of fluid layers overlying a rigid bottom. The medium may have range-dependent speed of sound and interface and bottom topography in the interior nonhomogeneous part of the waveguide, while in the far-field the interfaces and bottom are assumed to be horizontal and the problem separable. A nonlocal boundary condition based on the DtN map of the exterior problem is posed at the far-field artificial boundary. The problem is discretized by a standard Galerkin/finite element method and the resulting numerical scheme is implemented in a Fortran code that is interfaced with general mesh generation programs from the MODULEF finite element library and iterative linear solvers from QMRPACK. The code is tested on several small scale examples of acoustic propagation and scattering in the sea and its results are found to compare well with those of COUPLE.

This paper presents theoretical and computational results from our research on inverse scattering problems for acoustic waves in ocean environments. In particular, we discuss the determination of a three-dimensional (3-D) distributed inhomogeneity in a two-layered waveguide from scattered sound and the shape determination of an object in a stratified medium. Numerical examples are presented.

A hybrid three-dimensional (3-D), two-way sound propagation model (FDHB3D) is developed for solving 3-D backscattering problems. The FDHB3D model is based on a 3-D Radius-Marching Algorithm (RMA) incorporating a 2-D Two-way Coupling Approach (TCA) by means of a N×2-D procedure. Within a radius-independent space, a 3-D wave field is marched in the radial direction using the 3-D RMA. At the vertical boundaries, a 3-D reflected field is obtained by solving a 2-D Vertical Boundary Equation (VBE) using the 2-D TCA combined with a N×2-D procedure. Different approximations for the 3-D square root operator are compared. Errors arising from the azimuth discretization are analyzed. Numerical studies are performed to demonstrate the superior performance of the FDHB3D model, and to preliminarily reveal 3-D backscattering mechanisms. Studies show that the FDHB3D model can partly handle the azimuth coupling. It is also demonstrated that the diffraction mechanism dominates the backscattered field when the azimuth coupling is significant, while, the reflection mechanism dominates the backscattered field when the azimuth coupling is weak. It is concluded that the FDHB3D model may be applicable to solve specific 3-D backscattering problems in which the azimuth coupling is weak.