Journal
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS
Volume 28, Issue 2, Pages 257-262Publisher
PLEIADES PUBLISHING INC
DOI: 10.1134/S1061920821020102
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Funding
- Russian Foundation for Basic Research [18-3520081 mol a ved]
- POI FEBRAS Program POI FEBRAS Program Modeling of various-scale dynamical processes in the ocean [121021700341-2]
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This study examines the perturbations of acoustic normal modes in a shallow-water waveguide caused by bathymetry variations, discussing the formal calculation of derivatives of modal functions and eigenvalues with respect to water depth. The authors also explore the potential applications of these derivatives in sound propagation models based on the normal mode theory, showing that using the proposed formulas can significantly reduce the computational cost associated with sound pressure field computation in a range-dependent waveguide.
Perturbations of acoustic normal modes by bathymetry variations in a shallow-water waveguide are considered. The problem is reduced to the case of a potential perturbation for the stationary Schrodinger equation. The derivatives of the modal functions and eigenvalues with respect to water depth are formally calculated. Applications of such derivatives in sound propagation models based on the normal mode theory are discussed. It is shown that the computational cost associated with the sound pressure field computation in a range-dependent waveguide can be reduced by a factor of 5-10 by using the proposed formulas. DOI 10.1134/S1061920821020102
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