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Analytical solutions of shallow-water wave equations
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Date
2011
Author
Aydın, Baran
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Analytical solutions for the linear and nonlinear shallow-water wave equations are developed for evolution and runup of tsunamis –long waves– over one- and two-dimensional bathymetries. In one-dimensional case, the nonlinear equations are solved for a plane beach using the hodograph transformation with eigenfunction expansion or integral transform methods under different initial conditions, i.e., earthquake-generated waves, wind set-down relaxation, and landslide-generated waves. In two-dimensional case, the linear shallow-water wave equation is solved for a flat ocean bottom for initial waves having finite-crest length. Analytical verification of source focusing is presented. The role of focusing in unexpectedly high tsunami runup observations for the 17 July 1998 Papua New Guinea and 17 July 2006 Java Island, Indonesia tsunamis are investigated. Analytical models developed here can serve as benchmark solutions for numerical studies.
Subject Keywords
Water waves.
,
Wave equation.
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http://etd.lib.metu.edu.tr/upload/12613349/index.pdf
https://hdl.handle.net/11511/20610
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Graduate School of Natural and Applied Sciences, Thesis
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B. Aydın, “Analytical solutions of shallow-water wave equations,” Ph.D. - Doctoral Program, Middle East Technical University, 2011.