Journal of Computational Acoustics

A stable matrix method is presented for studying acoustic wave propagation in thick periodically layered anisotropic media at high frequencies. The method enables Floquet waves to be determined reliably based on the solutions to a generalized eigenproblem involving scattering matrix. The method thus overcomes the numerical difficulty in the standard eigenproblem involving cell transfer matrix, which occurs when the unit cell is thick or the frequency is high. With its numerical stability and reliability, the method is useful for analysis of periodic media with wide range of thickness at high frequencies.

A detailed study on the accuracy and reflection behavior of nonreflection boundary conditions is presented. To this end, a selection of five distinct nonreflecting boundary conditions is evaluated and the mechanisms which dominate the reflection properties of boundary conditions are identified based on a rigorous quantification of reflection levels. It is shown that the reflection behavior is significantly affected by the incident angle. The relation between the boundary condition effectiveness and the incident angle is investigated and the reflection rates as a function of the incident angle are quantified. Furthermore, the obtained results are used to predict the reflections from boundary conditions in general applications. It is shown that these predictions are reliable for different test cases.

In this paper a Control Volume Finite Element Method for harmonic acoustic problems is presented. A dispersion analysis for control volume constructed on Q1 finite elements is compared to Galerkin FEM. The spatial convergence is also given in an eigenfrequency determination process for a cavity. The application for exterior acoustic problems is also studied by dividing the whole field into inner and outer domains using a fictitious boundary. A control volume formulation is used to compute the inner field of the truncated problem, and several approaches are combined to describe the outer field behavior on the outside of the fictitious boundary. The task of coupling is easily implemented through the balance of local flux through polygonal volumes. A two-dimensional configuration with a circular interface demonstrates the validity of this approach.

Rough surface scattering theory is applied to the problem of estimating gravity-capillary wavenumber spectra from measurements of sea surface backscatter at high acoustic frequencies. Ensemble averaged scattering cross sections predicted by small-slope expansions are evaluated to examine the inversion of acoustic data assuming Bragg scatter. The ratio of the full fourth-order small-slope and Bragg predictions is found to exhibit a minimum value of ~ 2dB at moderate angles of incidence. At such angles, the corrections to perturbation theory depend weakly on acoustic frequency and environmental conditions. This latter finding indicates that only a modest effort is required to monitor sea surface conditions to estimate the correction. Corrections to Bragg predictions increase rapidly with increasing incidence angle and at high angles, the fourth-order contributions of the small-slope and extended small-slope expansions differ. This finding casts some doubt on the applicability of small-slope approximations to predict scattering at high-incidence angles.

A new hybrid algorithm of the depth solver for the wavenumber integration technique is derived. The global matrix method is adopted as the depth solver in the ocean, where there are sources and receivers present, and the reflectivity scheme is used for calculating the wave field of the porous ocean bottom. In order to hybridize both depth solvers, a novel technique has been developed where a virtual fluid layer with zero thickness is inserted between the ocean and the porous ocean bottom. This technique makes the hybrid algorithm simple to implement and compatible with any other depth solvers for the ocean bottom. Numerical simulation shows the proposed algorithm to work well.

We compare the results of a coupled mode method with those of a finite element method and also of COUPLE on two test problems of sound propagation and scattering in cylindrically symmetric, underwater, multilayered acoustic waveguides with range-dependent interface topographies. We observe, in general, very good agreement between the results of the three codes. In some cases in which the frequency of the harmonic point source is such that an eigenvalue of the local vertical problem remains small in magnitude and changes sign several times in the vicinity of the interface nonhomogeneity, the discrepancies between the results of the three codes increase, but remain small in absolute terms.

For ducted propagation in a waveguide when the source and receiver are placed close to the depth of the waveguide axis, there exist cusped caustics repeatedly along the axis. In neighborhoods of these cusped caustics, the interference of the wave fields that correspond to near-axial rays occurs. This results in the formation of a coherent structure (the axial wave) that propagates along the waveguide axis like a wave. In this paper, for the two-dimensional reference point source problem with the parabolic index of refraction squared the axial wave is represented in the form of a sum of the first normal modes and a remainder field. The mathematical framework is provided by two different representations of the acoustic field. The first one was obtained by Grigorieva et al.¹ It includes a sum of ray summands and the axial wave. The second representation including ray summands, a sum of the first normal modes, and a remainder field is derived in the present paper. For the remainder a simple formula including a special function is obtained. Numerical simulations are carried out for parameters corresponding to long-range ocean acoustic propagation experiments.