Mathematical treatment of wave propagation in acoustic waveguides with n curved interfaces |
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| Authors: | Jian-xin Zhu Peng Li |
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| Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | There are some curved interfaces in ocean acoustic waveguides. To compute wave propagation along the range with some marching
methods, a flattening of the internal interfaces and a transforming equation are needed. In this paper a local orthogonal
coordinate transform and an equation transformation are constructed to flatten interfaces and change the Helmholtz equation
as a solvable form. For a waveguide with a flat top, a flat bottom and n curved interfaces, the coefficients of the transformed Helmholtz equation are given in a closed formulation which can be
thought of as an extension of the formal work related to the equation transformation with two curved internal interfaces.
In the transformed horizontally stratified waveguide, the one-way reformulation based on the Dirichlet-to-Neumann (DtN) map
is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator
Riccati equation uses a large range step method to discretize the range variable and a truncated local eigenfunction expansion
to approximate the operators. This method is particularly useful for solving long range wave propagation problems in slowly
varying waveguides. Furthermore, the method can also be applied to wave propagation problems in acoustic waveguides associated
with varied density.
Project supported by the National Natural Science Foundation of China (No. 10571162) and the Natural Science Foundation of
Zhejiang Province, China (No. Y605181) |
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| Keywords: | Helmholtz equation Local orthogonal transform Dirichlet-to-Neumann (DtN) reformulation Marching method Curved interface Multilayer medium |
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