A multiscale model for weakly nonlinear shallow water waves over periodic bathymetry
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910814315741184 |
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| author | Ketcheson, David I. Lóczi, Lajos Russo, Giovanni |
| author_facet | Ketcheson, David I. Lóczi, Lajos Russo, Giovanni |
| contents | We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical experiments suggest a different behavior in the presence of periodic bathymetry. Starting from the first-order variable-coefficient hyperbolic system, we apply a multiple-scale perturbation approach in order to derive a system of constant-coefficient high-order partial differential equations whose solution approximates that of the original system. The high-order system turns out to be dispersive and exhibits solitary-wave formation, in close agreement with direct numerical simulations of the original system. We show that the constant-coefficient homogenized system can be used to study the properties of solitary waves and to conduct efficient numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_02603 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A multiscale model for weakly nonlinear shallow water waves over periodic bathymetry Ketcheson, David I. Lóczi, Lajos Russo, Giovanni Analysis of PDEs Atmospheric and Oceanic Physics We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical experiments suggest a different behavior in the presence of periodic bathymetry. Starting from the first-order variable-coefficient hyperbolic system, we apply a multiple-scale perturbation approach in order to derive a system of constant-coefficient high-order partial differential equations whose solution approximates that of the original system. The high-order system turns out to be dispersive and exhibits solitary-wave formation, in close agreement with direct numerical simulations of the original system. We show that the constant-coefficient homogenized system can be used to study the properties of solitary waves and to conduct efficient numerical simulations. |
| title | A multiscale model for weakly nonlinear shallow water waves over periodic bathymetry |
| topic | Analysis of PDEs Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2311.02603 |