Linear and Weakly Nonlinear Models of Wind Generated Surface Waves in Finite Depth
This work regards the extension of the Miles’ and Jeffreys’ theories of growth of wind-waves in water of finite depth. It is divided in two major sections. The first one corresponds to the surface water waves in a linear regimes and the second one to the surface water waver considered in a weak nonl...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Isfahan University of Technology
2017-01-01
|
| Series: | Journal of Applied Fluid Mechanics |
| Subjects: | |
| Online Access: | http://jafmonline.net/JournalArchive/download?file_ID=43835&issue_ID=245 |
| _version_ | 1828729617964335104 |
|---|---|
| author | A. Latifi M. A. Manna P. Montalvo M. Ruivo |
| author_facet | A. Latifi M. A. Manna P. Montalvo M. Ruivo |
| author_sort | A. Latifi |
| collection | DOAJ |
| description | This work regards the extension of the Miles’ and Jeffreys’ theories of growth of wind-waves in water of finite depth. It is divided in two major sections. The first one corresponds to the surface water waves in a linear regimes and the second one to the surface water waver considered in a weak nonlinear, dispersive and anti-dissipative regime. In the linear regime, we extend the Miles’ theory of wind wave amplification to finite depth. The dispersion relation provides a wave growth rate depending to depth. A dimensionless water depth parameter depending to depth and a characteristic wind speed, induces a family of curves representing the wave growth as a function of the wave phase velocity and the wind speed. We obtain a good agreement between our theoretical results and the data from the Australian Shallow Water Experiment as well as the data from the Lake George experiment. In a weakly nonlinear regime the evolution of wind waves in finite depth is reduced to an anti-dissipative Kortewegde Vries-Burgers equation and its solitary wave solution is exhibited. Anti-dissipation phenomenon accelerates the solitary wave and increases its amplitude which leads to its blow-up and breaking. Blow-up is a nonlinear, dispersive and anti-dissipative phenomenon which occurs in finite time. A consequence of anti-dissipation is that any solitary waves’ adjacent planes of constants phases acquire different velocities and accelerations and ends to breaking which occurs in finite space and in a finite time prior to the blow-up. It worth remarking that the theoretical amplitude growth breaking time are both testable in the usual experimental facilities. At the end, in the context of wind forced waves in finite depth, the nonlinear Schrödinger equation is derived and for weak wind inputs, the Akhmediev, Peregrine and Kuznetsov-Ma breather solutions are obtained. |
| first_indexed | 2024-04-12T14:36:03Z |
| format | Article |
| id | doaj.art-5439b58df4b240e48237a3bb0140f27d |
| institution | Directory Open Access Journal |
| issn | 1735-3572 |
| language | English |
| last_indexed | 2024-04-12T14:36:03Z |
| publishDate | 2017-01-01 |
| publisher | Isfahan University of Technology |
| record_format | Article |
| series | Journal of Applied Fluid Mechanics |
| spelling | doaj.art-5439b58df4b240e48237a3bb0140f27d2022-12-22T03:29:06ZengIsfahan University of TechnologyJournal of Applied Fluid Mechanics1735-35722017-01-0110618291843.Linear and Weakly Nonlinear Models of Wind Generated Surface Waves in Finite DepthA. Latifi0M. A. Manna1P. Montalvo2M. Ruivo3Department of Physics, Faculty of Sciences, Qom University of TechnologyUniversité Montpellier, Laboratoire Charles Coulomb UMR 5221Université Montpellier, Laboratoire Charles Coulomb UMR 5221Université Montpellier, Laboratoire Charles Coulomb UMR 5221This work regards the extension of the Miles’ and Jeffreys’ theories of growth of wind-waves in water of finite depth. It is divided in two major sections. The first one corresponds to the surface water waves in a linear regimes and the second one to the surface water waver considered in a weak nonlinear, dispersive and anti-dissipative regime. In the linear regime, we extend the Miles’ theory of wind wave amplification to finite depth. The dispersion relation provides a wave growth rate depending to depth. A dimensionless water depth parameter depending to depth and a characteristic wind speed, induces a family of curves representing the wave growth as a function of the wave phase velocity and the wind speed. We obtain a good agreement between our theoretical results and the data from the Australian Shallow Water Experiment as well as the data from the Lake George experiment. In a weakly nonlinear regime the evolution of wind waves in finite depth is reduced to an anti-dissipative Kortewegde Vries-Burgers equation and its solitary wave solution is exhibited. Anti-dissipation phenomenon accelerates the solitary wave and increases its amplitude which leads to its blow-up and breaking. Blow-up is a nonlinear, dispersive and anti-dissipative phenomenon which occurs in finite time. A consequence of anti-dissipation is that any solitary waves’ adjacent planes of constants phases acquire different velocities and accelerations and ends to breaking which occurs in finite space and in a finite time prior to the blow-up. It worth remarking that the theoretical amplitude growth breaking time are both testable in the usual experimental facilities. At the end, in the context of wind forced waves in finite depth, the nonlinear Schrödinger equation is derived and for weak wind inputs, the Akhmediev, Peregrine and Kuznetsov-Ma breather solutions are obtained.http://jafmonline.net/JournalArchive/download?file_ID=43835&issue_ID=245Surface waves; Wind waves; Interface waves; Rogue waves; Blow-up; Asymptotic models; Miles’s mechanism; Jeffreys’ mechanism. |
| spellingShingle | A. Latifi M. A. Manna P. Montalvo M. Ruivo Linear and Weakly Nonlinear Models of Wind Generated Surface Waves in Finite Depth Journal of Applied Fluid Mechanics Surface waves; Wind waves; Interface waves; Rogue waves; Blow-up; Asymptotic models; Miles’s mechanism; Jeffreys’ mechanism. |
| title | Linear and Weakly Nonlinear Models of Wind Generated Surface Waves in Finite Depth |
| title_full | Linear and Weakly Nonlinear Models of Wind Generated Surface Waves in Finite Depth |
| title_fullStr | Linear and Weakly Nonlinear Models of Wind Generated Surface Waves in Finite Depth |
| title_full_unstemmed | Linear and Weakly Nonlinear Models of Wind Generated Surface Waves in Finite Depth |
| title_short | Linear and Weakly Nonlinear Models of Wind Generated Surface Waves in Finite Depth |
| title_sort | linear and weakly nonlinear models of wind generated surface waves in finite depth |
| topic | Surface waves; Wind waves; Interface waves; Rogue waves; Blow-up; Asymptotic models; Miles’s mechanism; Jeffreys’ mechanism. |
| url | http://jafmonline.net/JournalArchive/download?file_ID=43835&issue_ID=245 |
| work_keys_str_mv | AT alatifi linearandweaklynonlinearmodelsofwindgeneratedsurfacewavesinfinitedepth AT mamanna linearandweaklynonlinearmodelsofwindgeneratedsurfacewavesinfinitedepth AT pmontalvo linearandweaklynonlinearmodelsofwindgeneratedsurfacewavesinfinitedepth AT mruivo linearandweaklynonlinearmodelsofwindgeneratedsurfacewavesinfinitedepth |