A Coupled-Mode Method for Acoustic Propagation and Scattering in Inhomogeneous Ocean Waveguides

2014 ◽  
Author(s):  
K. A. Belibassakis ◽  
G. A. Athanassoulis
Keyword(s):  
Bottom Topography ◽  
Three Dimensional ◽  
Acoustic Propagation ◽  
Local Mode ◽  
Scattering Problems ◽  
Coupled Mode ◽  
Cylindrically Symmetric ◽  
Present Solution ◽  
Mode Method ◽  
Additional Mode

We consider the problem of acoustic propagation and scattering in inhomogeneous waveguide governed by the Helmholtz equation. We focus on an ideal, cylindrically symmetric ocean waveguide, limited above by an acoustically soft boundary modelling the free surface, and below by a hard boundary modelling the impenetrable seabed with general bottom topography. The wave field is excited by a monochromatic point source, and thus, the present solution is equivalent to the construction of the Green’s function in the inhomogeneous domain. An improved coupled-mode method is developed, based on an enhanced local-mode series for the representation of the acoustic field, which includes an additional mode accounting for the effects of the bottom slope and curvature. The additional mode provides an implicit summation of the slowly convergent part of the series, rendering the remaining part to converge much faster, pemitting truncation of the modal expansions keeping only a few evanescent terms. Using the enhanced representation, in conjunction with an appropriate variational principle, a system of coupled-mode equations on the horizontal plane is derived for the determination of the complex modal-amplitude functions. Numerical results are presented including comparisons with analytical solutions illustrating the role and significance of the additional mode and the efficiency of the present coupled-mode tmodel, which can be naturally extended to treat propagation and scattering problems in three-dimensional, multi-layered ocean acoustic waveguides.

A Coupled-Mode, Phase-Resolving Model for the Transformation of Wave Spectrum Over Steep 3D Topography: A Parallel-Architecture Implementation

2005 ◽  
Author(s):  
Th. P. Gerosthathis ◽  
K. A. Belibassakis ◽  
G. A. Athanassoulis
Keyword(s):  
Incident Wave ◽  
Bottom Topography ◽  
Wave Spectrum ◽  
Three Dimensional ◽  
Parallel Architecture ◽  
Wave System ◽  
Directional Spectrum ◽  
Coupled Mode ◽  
Linear Waves ◽  
Velocity Pressure

The problem of transformation of the directional spectrum of an incident wave system over a region of strongly varying three-dimensional bottom topography is studied, in the context of linear theory. The Consistent Coupled-Mode Model (Athanassoulis and Belibassakis 1999, Belibassakis et al 2001) is exploited for the calculation of the linear transfer function, connecting the incident wave with the wave conditions at each point in the field. This model takes fully into account reflection, refraction and diffraction phenomena. The present approach permits the consistent transformation of any incident directional wave spectrum over a variable bathymetry region and the calculation of the spatial evolution of point spectra of all interesting wave quantities (free surface elevation, velocity, pressure), at every point in the domain. This approach can be extended to treat weakly non-linear waves.

scholarly journals Coupled mode theory of scattering by a cylindrically symmetric seamount

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150465 ◽  
Author(s):  
Ronald F. Pannatoni
Keyword(s):  
Three Dimensional ◽  
Numerical Procedure ◽  
Infinite Dimensional ◽  
Coupled Mode ◽  
Cylindrically Symmetric ◽  
Finite Dimensional ◽  
Time Harmonic ◽  
Acoustic Waveguides ◽  
Algebraic Formula ◽  
Stratified Ocean

The coupled-mode equations of Shevchenko are extended to three-dimensional irregular acoustic waveguides. These equations are solved for a model of a cylindrically symmetric seamount and a time-harmonic point source in a horizontally stratified ocean. An algebraic formula for the scattered field beyond the seamount is obtained from this solution. The formula is characterized by a set of infinite-dimensional matrices that are independent of the source. A stable numerical procedure is developed to compute finite-dimensional approximations to these matrices for use in truncated versions of the formula.

A Unified Coupled-Mode Approach to Nonlinear Waves in Finite Depth: Potential Flow

2008 ◽  
Author(s):  
G. A. Athanassoulis ◽  
K. A. Belibassakis
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Bottom Topography ◽  
Local Mode ◽  
Surface Mode ◽  
Nonlinear Water Waves ◽  
Coupled Mode ◽  
Wide Range ◽  
Sloping Bottom

A non-linear coupled-mode system of horizontal equations is presented, as derived from Luke’s (1967) variational principle, which models the evolution of nonlinear water waves in intermediate depth over a general bottom topography. The vertical structure of the wave field is represented by means of a complete local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional terms, the free-surface mode and the sloping-bottom mode, enabling to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. The present coupled-mode system fully accounts for the effects of non-linearity and dispersion, and has the following main features: (i) various standard models of water-wave propagation are recovered by appropriate simplifications, and (ii) it exhibits fast convergenge, and thus, a small number of modes (up to 5) are usually enough for the precise numerical solution, provided that the two new modes (the free-surface and the sloping-bottom ones) are included in the local-mode series. In the present work, the coupled-mode system is applied to the numerical investigation of families of steady traveling wave solutions in constant depth, corresponding to a wide range of water depths, ranging from intermediate to shallow-water wave conditions and its results are compared vs. Stokes and cnoidal wave theories, respectively. Also, numerical results are presented for waves propagating over variable bathymetry regions and compared with second-order Stokes theory and experimental data.

COUPLED MODE AND FINITE ELEMENT APPROXIMATIONS OF UNDERWATER SOUND PROPAGATION PROBLEMS IN GENERAL STRATIFIED ENVIRONMENTS

2008 ◽  
Vol 16 (01) ◽  
pp. 83-116 ◽  
Author(s):  
G. A. ATHANASSOULIS ◽  
K. A. BELIBASSAKIS ◽  
D. A. MITSOUDIS ◽  
N. A. KAMPANIS ◽  
V. A. DOUGALIS
Keyword(s):  
Finite Element ◽  
Sound Propagation ◽  
Test Problems ◽  
Underwater Sound ◽  
Finite Element Approximations ◽  
Coupled Mode ◽  
Cylindrically Symmetric ◽  
Mode Method ◽  
Acoustic Waveguides ◽  
Good Agreement

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.

ACOUSTIC THREE-DIMENSIONAL EFFECTS AROUND THE TAIWAN STRAIT: COMPUTATIONAL RESULTS

1999 ◽  
Vol 07 (01) ◽  
pp. 15-26 ◽  
Author(s):  
CHI-FANG CHEN ◽  
JANG-JIA LIN ◽  
DING LEE
Keyword(s):  
Field Data ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Propagation Model ◽  
Computational Results ◽  
Submarine Canyons ◽  
Offshore Area ◽  
Ocean Environment ◽  
The Taiwan Strait ◽  
Good Agreement

A set of experiments were performed in the offshore area off the coasts of Taiwan and three-dimensional (3-D) measurements recorded. The 3-D effect on underwater propagation due to azimuthal variation of bottom topography is studied for the offshore regions southwest of Taiwan, where submarine canyons exist. A 3-D acoustic propagation model, FOR3D, is used to detect the 3-D effect. Computational results show that the 3-D effect is more prominent along the axis of the canyon than across it. Calculations show a very good agreement with field data, which indicate that the 3-D effect exists in this realistic ocean environment.

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