 An analytical and numerical study of long wave run-up in U-shaped and V-shaped baysV.V. Garayshin, M.W. Harris, D.J. Nicolsky, E.N. Pelinovsky and A.V. Rybkin Applied Mathematics and Computation, 2016, vol. 279, issue C, 187-197 Abstract: By assuming the flow is uniform along the narrow long bays, the 2-D nonlinear shallow-water equations are reduced to a linear semi-axis variable-coefficient 1-D wave equation via the generalized Carrier–Greenspan transformation. The run-up of long waves in constantly sloping U-shaped and V-shaped bays is studied both analytically and numerically within the framework of the 1-D nonlinear shallow-water theory. An analytic solution, in the form of a double integral, to the resulting linear wave equation is obtained by utilizing the Hankel transform, and consequently the solution to the tsunami run-up problem is developed by applying the inverse generalized Carrier–Greenspan transform. The presented solution is a generalization of the solutions found by Carrier et al. (2003) and Didenkulova and Pelinovsky (2011) for the case of a plane beach and a parabolic bay, respectively. The shoreline dynamics in U-shaped and V-shaped bays are computed via a double integral through standard integration techniques. Keywords: Long wave run-up; Shallow water wave equations; Carrier–Greenspan transformation; Analytic solution (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:279:y:2016:i:c:p:187-197 DOI: 10.1016/j.amc.2016.01.005 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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