Acoustic pulse propagation in a non-ideal shallow-water model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918248717484032 |
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| author | Kaplun, Aleksandr Katsnelson, Boris |
| author_facet | Kaplun, Aleksandr Katsnelson, Boris |
| contents | This study develops a theoretical framework for modeling acoustic pulse propagation in a non-ideal shallow-water waveguide. We derive an ε-pseudodifferential operator (ε-PDO) formulation from the general three-dimensional wave equation, that accounts for vertical stratification, bottom interaction, and slow horizontal inhomogeneity. Using the operator separation of variables method and the WKB-ansatz, we obtain single-mode equations describing the evolution of amplitude and phase along rays. The approach incorporates non-self-adjoint operators to model energy leakage through the bottom and introduces a Hamiltonian formalism for eikonal and transport equations, enabling the computation of amplitude, time, and phase fronts. Analytical and numerical examples are provided for different boundary conditions, including Neumann (ideal), self-adjoint, and partially reflecting interfaces. The results extend previous semiclassical and ray-based theories of wave propagation by including dissipative effects and improving the physical realism of shallow-water acoustic modeling. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_09257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Acoustic pulse propagation in a non-ideal shallow-water model Kaplun, Aleksandr Katsnelson, Boris Mathematical Physics Atmospheric and Oceanic Physics Geophysics 34A30, 34A12, 34B24, 35L05, 35L20, 35S05, 35Q60, 70H05, 70H09, 76Q05, 81Q20 This study develops a theoretical framework for modeling acoustic pulse propagation in a non-ideal shallow-water waveguide. We derive an ε-pseudodifferential operator (ε-PDO) formulation from the general three-dimensional wave equation, that accounts for vertical stratification, bottom interaction, and slow horizontal inhomogeneity. Using the operator separation of variables method and the WKB-ansatz, we obtain single-mode equations describing the evolution of amplitude and phase along rays. The approach incorporates non-self-adjoint operators to model energy leakage through the bottom and introduces a Hamiltonian formalism for eikonal and transport equations, enabling the computation of amplitude, time, and phase fronts. Analytical and numerical examples are provided for different boundary conditions, including Neumann (ideal), self-adjoint, and partially reflecting interfaces. The results extend previous semiclassical and ray-based theories of wave propagation by including dissipative effects and improving the physical realism of shallow-water acoustic modeling. |
| title | Acoustic pulse propagation in a non-ideal shallow-water model |
| topic | Mathematical Physics Atmospheric and Oceanic Physics Geophysics 34A30, 34A12, 34B24, 35L05, 35L20, 35S05, 35Q60, 70H05, 70H09, 76Q05, 81Q20 |
| url | https://arxiv.org/abs/2511.09257 |