Initial value problem solution of nonlinear shallow water-wave equations

Date

2006-10-06

Author

Kanoğlu, Utku
Synolakis, Costas

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The initial value problem solution of the nonlinear shallow water-wave equations is developed under initial waveforms with and without velocity. We present a solution method based on a hodograph-type transformation to reduce the nonlinear shallow water-wave equations into a second-order linear partial differential equation and we solve its initial value problem. The proposed solution method overcomes earlier limitation of small waveheights when the initial velocity is nonzero, and the definition of the initial conditions in the physical and transform spaces is consistent. Our solution not only allows for evaluation of differences in predictions when specifying an exact initial velocity based on nonlinear theory and its linear approximation, which has been controversial in geophysical practice, but also helps clarify the differences in runup observed during the 2004 and 2005 Sumatran tsunamigenic earthquakes.

Subject Keywords

Sloping beach, Run-up, Tsunami, Amplitude, Evolutİon, Model

URI

https://hdl.handle.net/11511/48421

Collections

Department of Engineering Sciences, Article