General initial value problem for the nonlinear shallow water equations: Runup of long waves on sloping beaches and bays |
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| Authors: | Dmitry Nicolsky Efim Pelinovsky Amir Raz Alexei Rybkin |
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| Affiliation: | 1. Geophysical Institute, University of Alaska Fairbanks, USA;2. Nizhny Novgorod State Technical University n.a. R. Alekseev, Russia;3. Special Research Bureau for Automation of Marine Researches, Yuzhno-Sakhalinsk, Russia;4. Institute of Applied Physics, Nizhny Novgorod, Russia;5. Department of Mathematics and Statistics, University of Alaska Fairbanks, USA |
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| Abstract: | ![]()
We formulate a new approach to solving the initial value problem of the shallow water-wave equations utilizing the famous Carrier–Greenspan transformation (Carrier and Greenspan (1957) [9]). We use a Taylor series approximation to deal with the difficulty associated with the initial conditions given on a curve in the transformed space. This extends earlier solutions to waves with near shore initial conditions, large initial velocities, and in more complex U-shaped bathymetries; and allows verification of tsunami wave inundation models in a more realistic 2-D setting. |
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| Keywords: | Nonlinear shallow water equations Tsunami Inclined channels Carrier–Greenspan transformation |
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