Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths

Imre Ferenc Barna, Mihály András Pocsai and Laszlo Matyas ()
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Imre Ferenc Barna: Wigner Research Centre for Physics, Konkoly–Thege Miklós út 29-33, H-1121 Budapest, Hungary
Mihály András Pocsai: Wigner Research Centre for Physics, Konkoly–Thege Miklós út 29-33, H-1121 Budapest, Hungary

Mathematics, 2022, vol. 10, issue 13, 1-16

Abstract: 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.

Keywords: partial differential equations; conservation laws and constitutive relations; tsunamis; physical oceanography; ocean waves and oscillations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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