Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths
We investigate a hydrodynamic equation system which—with some approximation—is capable of describing the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions of how the wave height and velocity behave in time and space for constant and linear...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/13/2311 |
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| author | Imre Ferenc Barna Mihály András Pocsai László Mátyás |
| author_facet | Imre Ferenc Barna Mihály András Pocsai László Mátyás |
| author_sort | Imre Ferenc Barna |
| collection | DOAJ |
| description | We investigate a hydrodynamic equation system which—with some approximation—is capable of describing the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions of how the wave height and velocity behave in time and space for constant and linear seabed functions. First, we study waves on open water, where the seabed can be considered relatively constant, sufficiently far from the shore. We found original shape functions for the ocean waves. In the second part of the study, we also consider a seabed which is oblique. Most of the solutions can be expressed with special functions. Finally, we apply the most common traveling wave Ansatz and present relative simple, although instructive solutions as well. |
| first_indexed | 2024-03-09T10:26:49Z |
| format | Article |
| id | doaj.art-041b91dbb42247f19529096e2e6d3818 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:26:49Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-041b91dbb42247f19529096e2e6d38182023-12-01T21:35:36ZengMDPI AGMathematics2227-73902022-07-011013231110.3390/math10132311Time-Dependent Analytic Solutions for Water Waves above Sea of Varying DepthsImre Ferenc Barna0Mihály András Pocsai1László Mátyás2Wigner Research Centre for Physics, Konkoly–Thege Miklós út 29-33, H-1121 Budapest, HungaryWigner Research Centre for Physics, Konkoly–Thege Miklós út 29-33, H-1121 Budapest, HungaryDepartment of Bioengineering, Faculty of Economics, Socio-Human Sciences and Engineering, Sapientia Hungarian University of Transylvania, Libertătii Sq. 1, 530104 Miercurea Ciuc, RomaniaWe investigate a hydrodynamic equation system which—with some approximation—is capable of describing the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions of how the wave height and velocity behave in time and space for constant and linear seabed functions. First, we study waves on open water, where the seabed can be considered relatively constant, sufficiently far from the shore. We found original shape functions for the ocean waves. In the second part of the study, we also consider a seabed which is oblique. Most of the solutions can be expressed with special functions. Finally, we apply the most common traveling wave Ansatz and present relative simple, although instructive solutions as well.https://www.mdpi.com/2227-7390/10/13/2311partial differential equationsconservation laws and constitutive relationstsunamisphysical oceanographyocean waves and oscillations |
| spellingShingle | Imre Ferenc Barna Mihály András Pocsai László Mátyás Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths Mathematics partial differential equations conservation laws and constitutive relations tsunamis physical oceanography ocean waves and oscillations |
| title | Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths |
| title_full | Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths |
| title_fullStr | Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths |
| title_full_unstemmed | Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths |
| title_short | Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths |
| title_sort | time dependent analytic solutions for water waves above sea of varying depths |
| topic | partial differential equations conservation laws and constitutive relations tsunamis physical oceanography ocean waves and oscillations |
| url | https://www.mdpi.com/2227-7390/10/13/2311 |
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