A Weakly Nonlinear System for Waves and Sheared Currents over Variable Bathymetry
The wave–current–seabed interaction problem is studied by using a coupled-mode system developed for modeling wave scattering by non-homogeneous, sheared currents in variable bathymetry regions. The model is based on a modal series expansion of wave velocity based on vertical eigenfunctions, dependen...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Journal of Marine Science and Engineering |
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| Online Access: | https://www.mdpi.com/2077-1312/12/3/509 |
| _version_ | 1797240424464646144 |
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| author | Julien Touboul Veronica Morales-Marquez Kostas Belibassakis |
| author_facet | Julien Touboul Veronica Morales-Marquez Kostas Belibassakis |
| author_sort | Julien Touboul |
| collection | DOAJ |
| description | The wave–current–seabed interaction problem is studied by using a coupled-mode system developed for modeling wave scattering by non-homogeneous, sheared currents in variable bathymetry regions. The model is based on a modal series expansion of wave velocity based on vertical eigenfunctions, dependent on local depth and flow parameters, including propagating and evanescent modes. The latter representation is able to accurately satisfy the wave flow continuity condition and the no-entrance boundary condition on the sloping parts of the seabed. A new derivation of a simplified nonlinear system is introduced using decomposition to a mean flow and a perturbative wave field. To force the system to consider incoming waves at the inlet, boundary knowledge of periodic, travelling nonlinear water waves over a flat bottom is required. For this purpose, specific solutions are derived using the semi-analytical method based on the stream function formulation, for cases of water waves propagating above linearly and exponentially sheared currents. Results obtained by the application of the CMS concerning the propagation of waves and currents—in particular, examples characterized by depth inhomogeneities—are presented and discussed, illustrating the applicability and performance of the method. |
| first_indexed | 2024-04-24T18:07:13Z |
| format | Article |
| id | doaj.art-9655f0b13c734d33a0195693e9d17636 |
| institution | Directory Open Access Journal |
| issn | 2077-1312 |
| language | English |
| last_indexed | 2024-04-24T18:07:13Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Marine Science and Engineering |
| spelling | doaj.art-9655f0b13c734d33a0195693e9d176362024-03-27T13:49:28ZengMDPI AGJournal of Marine Science and Engineering2077-13122024-03-0112350910.3390/jmse12030509A Weakly Nonlinear System for Waves and Sheared Currents over Variable BathymetryJulien Touboul0Veronica Morales-Marquez1Kostas Belibassakis2École Centrale Méditerranée, Aix Marseille Université, CNRS, IRPHE UMR 7342, 13384 Marseille, FranceUniversity of Toulon, Aix Marseille University, CNRS/INSU, IRD, MIO UM 110, Mediterranean Institute of Oceanography, 83130 La Garde, FranceSchool of Naval Architecture and Marine Engineering, National Technical University of Athens, Zografos, 15773 Athens, GreeceThe wave–current–seabed interaction problem is studied by using a coupled-mode system developed for modeling wave scattering by non-homogeneous, sheared currents in variable bathymetry regions. The model is based on a modal series expansion of wave velocity based on vertical eigenfunctions, dependent on local depth and flow parameters, including propagating and evanescent modes. The latter representation is able to accurately satisfy the wave flow continuity condition and the no-entrance boundary condition on the sloping parts of the seabed. A new derivation of a simplified nonlinear system is introduced using decomposition to a mean flow and a perturbative wave field. To force the system to consider incoming waves at the inlet, boundary knowledge of periodic, travelling nonlinear water waves over a flat bottom is required. For this purpose, specific solutions are derived using the semi-analytical method based on the stream function formulation, for cases of water waves propagating above linearly and exponentially sheared currents. Results obtained by the application of the CMS concerning the propagation of waves and currents—in particular, examples characterized by depth inhomogeneities—are presented and discussed, illustrating the applicability and performance of the method.https://www.mdpi.com/2077-1312/12/3/509wave–current interactionsheared currentvariable bathymetrycoupled modes |
| spellingShingle | Julien Touboul Veronica Morales-Marquez Kostas Belibassakis A Weakly Nonlinear System for Waves and Sheared Currents over Variable Bathymetry Journal of Marine Science and Engineering wave–current interaction sheared current variable bathymetry coupled modes |
| title | A Weakly Nonlinear System for Waves and Sheared Currents over Variable Bathymetry |
| title_full | A Weakly Nonlinear System for Waves and Sheared Currents over Variable Bathymetry |
| title_fullStr | A Weakly Nonlinear System for Waves and Sheared Currents over Variable Bathymetry |
| title_full_unstemmed | A Weakly Nonlinear System for Waves and Sheared Currents over Variable Bathymetry |
| title_short | A Weakly Nonlinear System for Waves and Sheared Currents over Variable Bathymetry |
| title_sort | weakly nonlinear system for waves and sheared currents over variable bathymetry |
| topic | wave–current interaction sheared current variable bathymetry coupled modes |
| url | https://www.mdpi.com/2077-1312/12/3/509 |
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