Ahmad T. Abawi

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.

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.

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 Greens 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.

Calculation of scattering from underwater targets using the equivalent source technique

The equivalent source technique is a method of computing scattering and radiation from a target by replacing the target by a distribution of discrete sources, whose complex amplitudes are determined by applying the boundary condition on the total field. The advantage of using this method, particularly in underwater acoustics, is that it essentially transforms the scattering and propagation problems into just a propagation problem, where the target can be treated as a distribution of sources rather than an impedance discontinuity. In this paper the equivalent source technique and different propagation models such as the normal mode, the parabolic equation and the fast field method are used to compute scattering from various target shapes/properties placed in the ocean waveguide. The results are compared with those obtained from other numerical codes. In addition, the relationship between the equivalent source technique with boundary element method (BEM) and the method of moments (MoM) is investigated.

Modeling the acoustic response of elastic targets in a layered medium using the coupled finite element/boundary element method

The fluid-structure interaction technique provides a paradigm for solving scattering from elastic targets embedded in a fluid by a combination of finite and boundary element methods. In this technique, the finite element method is used to compute the target’s elastic response and the boundary element method with the appropriate Green’s function is used to compute the field in the exterior medium. The two methods are coupled at the surface of the target by imposing the continuity of pressure and normal displacement. This results in a boundary element equation that can be used to compute the scattered field anywhere in the surrounding environment. This method reduces a finite element problem to a boundary element one with drastic reduction in the number of unknowns, which translates to a significant reduction in numerical cost. In this talk, the derivation of the technique will be outlined; the method will be applied to compute scattering from various targets, including unexploded ordnance (UXO) in complex ...

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 fluid–structure interaction technique specialized to axially symmetric targets

The fluid–structure interaction technique provides a paradigm for solving scattering from elastic targets embedded in a fluid by a combination of finite and boundary element methods. In this technique, the finite element method is used to compute the target’s impedance matrix and the Helmholtz–Kirchhoff integral with the appropriate Green’s function is used to represent the field in the exterior medium. The two equations are coupled at the surface of the target by imposing the continuity of pressure and normal displacement. This results in a Helmholtz–Kirchhoff boundary element equation that can be used to compute the scattered field anywhere in the surrounding environment. This method reduces a finite element problem to a boundary element one with drastic reduction in the number of unknowns, which translates to a significant reduction in numerical cost. This method was developed and tested for general 3D targets. In this paper, the method is specialized to axially symmetric targets, which provides furthe...

Low frequency scattering from elastic objects embedded in a waveguide by the finite element technique.

Computation of scattering from an object in a waveguide is a challenging task because of the enormous size of the computational domain. It requires the solution of the wave equation by simultaneously satisfying the boundary conditions on the surface of the object and the boundaries of the waveguide. While the finite element solution of scattering from an object in free space can be managed by limiting the size of the computational domain by the use of infinite elements or perfectly matched layers for an object in a waveguide, the waveguide itself is part of the computational domain. Since an accurate solution requires that the computational domain be discretized at least at one‐tenth of the acoustic wavelength for a computational domain tens or hundreds of wavelength large, this results in very large systems of equations, whose solution is a daunting numerical task. To cope with the numerical complexity, in this paper we use the principles of fluid‐structure interaction to compute scattering from the obje...

Exact and approximate techniques for scattering from targets embedded in a layered medium.

To be able to accurately compute scattering from a target embedded in a layered medium (waveguide), the scattering and propagation problems must be solved as a single boundary value problem. This is accomplished by solving the wave equation in an environment that contains both the target and the waveguide and satisfying boundary conditions on the surface of the target and the boundaries of the waveguide. One way that this can be accomplished is by the use of the virtual source technique, which replaces the target with a collection of sources whose amplitudes are determined from the boundary conditions on the surface of the target. This method converts the problem of scattering from a target in a waveguide to a multisource propagation problem. In this paper, the virtual source technique is used to compute scattering from a target in a waveguide and various ways to speed up computation are examined. These include the use of various propagation models to propagate the field produced by the virtual sources to...

Quantitative Performance Comparison Among Processors in MFP

Data on a tilted line a array (TLA) from the 1996 Shallow Water Cell Experiment (SWellEx-96), which was performed in 200 meters of water over a relatively flat bottom, are used to quantitatively evaluate the performance of processors used in matched field processing (MFP). The MVDR processor, the dominant-mode rejection processor and the partially-adaptive reduced-rank processor have been evaluated using data on a tilted line array (TLA). According to this evaluation, the MVDR processor with white noise gian constraint (WNGC) has the best performance, followed by the dominant-mode rejection processor, the partially-adaptive reduced-rank processor and the linear processor.