Abstract
Numerous sound propagation models in underwater acoustics are based on the representation of a sound field in the form of a decomposition over normal modes. In the framework of such models, the calculation of the field in a range-dependent waveguide (as well as in the case of 3D problems) requires the computation of normal modes for every point within the area of interest (that is, for each pair of horizontal coordinates x,y). This procedure is often responsible for the lion’s share of total computational cost of the field simulation. In this study, we present formulae for perturbation of eigenvalues and eigenfunctions of normal modes under the water depth variations in a shallow-water waveguide. These formulae can reduce the total number of mode computation instances required for a field calculation by a factor of 5–10. We also discuss how these formulae can be used in a combination with a wide-angle mode parabolic equation. The accuracy of such combined model is validated in a series of numerical examples.
Highlights
Numerous sound propagation models in underwater acoustics are based on the representation of a sound field in the form of a decomposition over normal modes
Computational technique based on the normal modes theory is widely used in underwater acoustics and its applications that cover a large area of marine sciences [1,2,3]
Sound field in a 3D oceanic waveguide formed by the sea surface z = 0 and sea bottom z = h( x, y) can be represented in the form of the expansion
Summary
The main goal of the present study is to improve the computational efficiency of sound propagation models based on the normal modes theory that rely on representation of acoustic field in the form (1). The Dirichlet boundary conditions at the endpoints of the interval [0, H ] in Equation (3) ensure that the problem has purely discrete spectrum consisting of a countable set of real eigenvalues k2j , j = 1, 2,. We assume that they are ordered in such a way that k2j ≥ k2j+1 for all j. . The respective eigenfunctions φj (z) are obviously continuous on [0, H ], and their restrictions φj | I1,2 to the intervals I1,2 belong to spaces C2 ( I1,2 ), respectively In this case, k j and φj can be considered functions of h (while the latter is in turn a function of horizontal coordinates x, y).
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