General initial value problem for the nonlinear shallow water equations: Runup of long waves on sloping beaches and bays

Publication date: Available online 23 July 2018Source: Physics Letters AAuthor(s): Dmitry Nicolsky, Efim Pelinovsky, Amir Raz, Alexei RybkinAbstractWe 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.

Source: Physics Letters A - July 23, 2018 Category: Physics Source Type: research