A three-dimensional, longitudinally-invariant finite element model for acoustic propagation in shallow water waveguides

Abstract

A three-dimensional, longitudinally-invariant finite element (FE) model for shallow water acoustic propagation is constructed through a cosine transform of a series of two-dimensional FE models at different values of the out-of-plane wavenumber. An innovative wavenumber sampling method is developed that efficiently captures the essential components of the integral as the out-of-plane wave number approaches the water wavenumber. The method is validated by comparison with benchmark solutions of two shallow water waveguide environments: a flat range independent case and a benchmark wedge.

Long range incoherent seafloor reverberation model based on coupled normal mode method

“…에서는 해석적 방법 [3,4] 을 이용하거나 음선 이론, [5][6][7] 양방향 포물선 방정식법, [8] 유한요소법, [9] 정상모드 법 [10][11][12][13][14][15] 을 이용한 잔향음 모델이 제시되었다.…”

Normal Mode Analysis of Three-Dimensional Propagation Over a Small-Slope Cosine Shaped Hill

“…For this comparison, a reference solution was calculated using a FEM model. 29 The environment for this evaluation is identical to the environment described in Sec. 3, with the exception that the water depth described by Eq.…”

“…Because the integrand of the cosine transform was found to be much more oscillatory near k y = k, the wavenumber space was sampled more finely in the vicinity of k. The spacing near k was prescribed by an offset gamma cumulative distribution function (CDF) with linear sampling for wavenumbers, k y > 1.01k. 29 The shape of the gamma CDF allows for finer sampling in the highly oscillatory region and coarser sampling in smoother regions, saving computational time and resources. For this model, linear spacing would have required 1,256,600 evaluations to achieve the same accuracy as the 26,696 evaluations used in the nonuniform spacing scheme.…”

“…The solution is obtained by applying a cosine transform to eliminate the range-and bearing-independent dimension. 29 The technique is applied to calculate propagation over the infinite cosine hill and the result is compared to the solution produced by the approximate normal mode/parabolic equation hybrid model.…”

“…The approximate solution is compared to a solution obtained with the finite element method (FEM) 29 to evaluate the accuracy of the solution in light of assumptions made in formulating the model. Then the calculated transmission loss is interpreted in terms of a modal decomposition of the field, and the 3D coupled-mode solution is compared to adiabatic and N × 2D solutions to assess the relative importance of horizontal refraction and mode-coupling effects.…”