Dmitry Nicolsky | Searcharxiv

arXiv2020

General Initial Value Problem for the Nonlinear Shallow Water Equations: Runup of Long Waves on Sloping Beaches and Bays

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.

physics.flu-dyn↗

arXiv2018

A response function approach for rapid far-field tsunami forecasting

Predicting tsunami impacts at remote coasts largely relies on tsunami en-route measurements in an open ocean. In this work, these measurements are used to generate instant tsunami predictions in deep water and near the coast. The predictions are generated as a response or a combination of responses to one or more tsunameters, with each response obtained as a convolution of real-time tsunameter measurements and a pre-computed Pulse Response Function (PRF). Practical implementation of this method requires tables of PRFs in a 3D parameter space: earthquake location - tsunameter - forecasted site. Examples of hindcasting the 2010 Chilean and the 2011 Tohoku-Oki tsunamis along the US West Coast and beyond demonstrated high accuracy of the suggested technology in application to trans-Pacific seismically-generated tsunamis.

physics.geo-ph↗