General Initial Value Problem for the Nonlinear Shallow Water Equations: Runup of Long Waves on Sloping Beaches and Bays
Fluid Dynamics
2020-08-10 v1 Mathematical Physics
math.MP
Abstract
We formulate a new approach to solving the initial value problem of the shallow water-wave equations utilizing the famous Carrier-Greenspan transformation [G. Carrier and H. Greenspan, J. Fluid Mech. 01, 97 (1957)]. 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.
Keywords
Cite
@article{arxiv.2008.02843,
title = {General Initial Value Problem for the Nonlinear Shallow Water Equations: Runup of Long Waves on Sloping Beaches and Bays},
author = {Dmitry Nicolsky and Efim Pelinovsky and Amir Raz and Alexei Rybkin},
journal= {arXiv preprint arXiv:2008.02843},
year = {2020}
}