Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation
Linear wave theory is a simple theory that researchers and engineers often use to study a wave in deep, intermediate, and shallow water regions. Many researchers mostly used it over the horizontal flat seabed, but in actual conditions, sloping seabed always exists, although mild. In this research, w...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
UIN Sunan Gunung Djati Bandung, Mathematics Department
2022-09-01
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| Series: | Kubik |
| Subjects: | |
| Online Access: | https://journal.uinsgd.ac.id/index.php/kubik/article/view/18419 |
| _version_ | 1797972142214610944 |
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| author | Faizal Ade Rahmahuddin Abdullah Elvi Syukrina Erianto |
| author_facet | Faizal Ade Rahmahuddin Abdullah Elvi Syukrina Erianto |
| author_sort | Faizal Ade Rahmahuddin Abdullah |
| collection | DOAJ |
| description | Linear wave theory is a simple theory that researchers and engineers often use to study a wave in deep, intermediate, and shallow water regions. Many researchers mostly used it over the horizontal flat seabed, but in actual conditions, sloping seabed always exists, although mild. In this research, we try to model a wave over a mild sloping seabed by linear wave theory and analyze the influence of the seabed’s slope on the solution of the model. The model is constructed from Laplace and Bernoulli equations together with kinematic and dynamic boundary conditions. We used the result of the analytical solution to find the relation between propagation speed, wavelength, and bed slope through the dispersion relation. Because of the difference in fluid dispersive character for each water region, we also determined dispersion relation approximation by modifying the hyperbolic tangent form into hyperbolic sine-cosine and exponential form, then approximated it with Padé approximant. As the final result, exponential form modification with Padé approximant had the best agreement to exact dispersion relation equation then direct hyperbolic tangent form. |
| first_indexed | 2024-04-11T03:43:45Z |
| format | Article |
| id | doaj.art-f15369917999443eb814d636750e1edc |
| institution | Directory Open Access Journal |
| issn | 2338-0896 2686-0341 |
| language | English |
| last_indexed | 2024-04-11T03:43:45Z |
| publishDate | 2022-09-01 |
| publisher | UIN Sunan Gunung Djati Bandung, Mathematics Department |
| record_format | Article |
| series | Kubik |
| spelling | doaj.art-f15369917999443eb814d636750e1edc2023-01-02T03:25:20ZengUIN Sunan Gunung Djati Bandung, Mathematics DepartmentKubik2338-08962686-03412022-09-017111010.15575/kubik.v7i1.184196225Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation ApproximationFaizal Ade Rahmahuddin Abdullah0Elvi Syukrina Erianto1ID Scoupus: 57211667630; Marine Disaster Research Center, Korea Institute of Ocean Science and Technology (KIOST)UIN Sunan Gunung Djati BandungLinear wave theory is a simple theory that researchers and engineers often use to study a wave in deep, intermediate, and shallow water regions. Many researchers mostly used it over the horizontal flat seabed, but in actual conditions, sloping seabed always exists, although mild. In this research, we try to model a wave over a mild sloping seabed by linear wave theory and analyze the influence of the seabed’s slope on the solution of the model. The model is constructed from Laplace and Bernoulli equations together with kinematic and dynamic boundary conditions. We used the result of the analytical solution to find the relation between propagation speed, wavelength, and bed slope through the dispersion relation. Because of the difference in fluid dispersive character for each water region, we also determined dispersion relation approximation by modifying the hyperbolic tangent form into hyperbolic sine-cosine and exponential form, then approximated it with Padé approximant. As the final result, exponential form modification with Padé approximant had the best agreement to exact dispersion relation equation then direct hyperbolic tangent form.https://journal.uinsgd.ac.id/index.php/kubik/article/view/18419linear wave, mild sloping seabed, dispersion relation approximation, velocity potential |
| spellingShingle | Faizal Ade Rahmahuddin Abdullah Elvi Syukrina Erianto Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation Kubik linear wave, mild sloping seabed, dispersion relation approximation, velocity potential |
| title | Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation |
| title_full | Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation |
| title_fullStr | Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation |
| title_full_unstemmed | Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation |
| title_short | Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation |
| title_sort | modeling a wave on mild sloping bottom topography and its dispersion relation approximation |
| topic | linear wave, mild sloping seabed, dispersion relation approximation, velocity potential |
| url | https://journal.uinsgd.ac.id/index.php/kubik/article/view/18419 |
| work_keys_str_mv | AT faizaladerahmahuddinabdullah modelingawaveonmildslopingbottomtopographyanditsdispersionrelationapproximation AT elvisyukrinaerianto modelingawaveonmildslopingbottomtopographyanditsdispersionrelationapproximation |