Specular-reflection contributions to static and dynamic radiation forces on circular cylinders.

Interest in the response of highly reflecting objects in water to modulated acoustical radiation forces makes it appropriate to consider contributions to such forces from perfectly reflecting objects to provide insight into radiation forces. The acoustic illumination can have wavelengths much smaller than the object's size, and objects of interest may have complicated shapes. Here, the specular contribution to the oscillating radiation force on an infinite circular cylinder at normal incidence is considered for double-sideband-suppressed carrier-modulated acoustic illumination. The oscillatory magnitude of the specular force decreases monotonically with increasing modulation frequency, and the phase of the oscillating force depends on the relative phase of the sidebands. The phase dependence on the modulation frequency can be reduced with the appropriate selection of a sideband relative-phase parameter. That is a consequence of the significance of rays that are incident on the cylinder having small impact parameters that are nearly backscattered. For one choice of a relative sideband phase, a prior partial wave series (PWS) solution is available, which supports the specular analysis when the PWS is evaluated for a rigid cylinder. The importance of specular contributions for aluminum cylinders in water is noted. A specular analysis for an analogous spherical reflector is also summarized.

Coupled finite element/boundary element formulation for scattering from axially-symmetric objects in three dimensions.

The fluid-structure interaction technique provides a paradigm for solving scattering from elastic structures embedded in an environment characterized by a Green's function, by a combination of finite and boundary element methods. In this technique, the finite element method is used to discretize the equations of motion for the structure and the Helmholtz-Kirchhoff integral with the appropriate Green's function is used to produce the discrete pressure field in the exterior medium. The two systems of equations are coupled at the surface of the structure by imposing the continuity of pressure and normal particle velocity. The present method condenses the finite element model so that finally only the boundary element problem needs to be solved. This results in a significant reduction in the number of unknowns and hence a much lower cost. In this paper, the fluid-structure interaction method is specialized to axially-symmetric objects for non-axially-symmetric loading in free space using a circumferential Fourier expansion of the fields. The specialization of the method to axially-symmetric objects results in even further significant reductions in computation. The method is validated using well-known benchmark solutions. A derivation of the method for an arbitrarily-shaped elastic structure embedded in an arbitrary environment characterized by a Green's function is given in the Appendix.

Kirchhoff scattering from non-penetrable targets modeled as an assembly of triangular facets.

Frequency and time domain solutions for the scattering of acoustic waves from an arbitrarily shaped target using the Kirchhoff approximation are developed. In this method, the scattering amplitude is analytically evaluated on a single triangle and scattering from a triangularly facetted target is computed by coherently summing the contributions from all the triangles that make up its surface. In the frequency domain, the solution is expressed in terms of regular (non-singular) functions, which only require the knowledge of the directions of the incident and scattered fields, the edge vectors for the triangles and position vectors to one of their vertices. To derive representations using regular functions in the time domain, the scattered signal is expressed by different expressions for various limiting cases. The frequency domain solution is validated by comparing its results to the solutions of problems for which the Kirchhoff approximation has analytic solutions. In order of increasing complexity, they include the square plate, the circular plate, the finite cylinder and the sphere. The time domain solution is validated by comparing it to the time domain solution of the Kirchhoff approximation for a rigid sphere.

The use of the virtual source technique in computing scattering from periodic ocean surfaces.

In this paper the virtual source technique is used to compute scattering of a plane wave from a periodic ocean surface. The virtual source technique is a method of imposing boundary conditions using virtual sources, with initially unknown complex amplitudes. These amplitudes are then determined by applying the boundary conditions. The fields due to these virtual sources are given by the environment Green's function. In principle, satisfying boundary conditions on an infinite surface requires an infinite number of sources. In this paper, the periodic nature of the surface is employed to populate a single period of the surface with virtual sources and m surface periods are added to obtain scattering from the entire surface. The use of an accelerated sum formula makes it possible to obtain a convergent sum with relatively small number of terms (∼40). The accuracy of the technique is verified by comparing its results with those obtained using the integral equation technique.

Propagation in an elastic wedge using the virtual source technique.

The virtual source technique, which is based on the boundary integral method, provides the means to impose boundary conditions on arbitrarily shaped boundaries by replacing them by a collection of sources whose amplitudes are determined from the boundary conditions. In this paper the virtual source technique is used to model propagation of waves in a range-dependent ocean overlying an elastic bottom with arbitrarily shaped ocean-bottom interface. The method is applied to propagation in an elastic Pekeris waveguide, an acoustic wedge, and an elastic wedge. In the case of propagation in an elastic Pekeris waveguide, the results agree very well with those obtained from the wavenumber integral technique, as they do with the solution of the parabolic equation (PE) technique in the case of propagation in an acoustic wedge. The results for propagation in an elastic wedge qualitatively agree with those obtained from an elastic PE solution.

An energy-conserving one-way coupled mode propagation model.

The equations of motion for pressure and displacement fields in a waveguide have been used to derive an energy-conserving, one-way coupled mode propagation model. This model has three important properties: First, since it is based on the equations of motion, rather than the wave equation, instead of two coupling matrices, it only contains one coupling matrix. Second, the resulting coupling matrix is anti-symmetric, which implies that the energy among modes is conserved. Third, the coupling matrix can be computed using the local modes and their depth derivatives. The model has been applied to two range-dependent cases: Propagation in a wedge, where range dependence is due to variations in water depth and propagation through internal waves, where range dependence is due to variations in water sound speed. In both cases the solutions are compared with those obtained from the parabolic equation (PE) method.