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All Journal SITEKIN: Jurnal Sains, Teknologi dan Industri KUBIK: Jurnal Publikasi Ilmiah Matematika
Elvi Syukrina Erianto
UIN Sunan Gunung Djati Bandung
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Industrial & Manufacturing Engineering Mathematics Other

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Journal : KUBIK: Jurnal Publikasi Ilmiah Matematika

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Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation Faizal Ade Rahmahuddin Abdullah; Elvi Syukrina Erianto
KUBIK Vol 7, No 1 (2022): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v7i1.18419

Abstract

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.
Co-Authors Faizal Ade Rahmahuddin Abdullah Mia Siti Khumaeroh