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Regular version of the site

Article

Runup of nonlinear long waves in trapezoidal bays: 1-D analytical theory and 2-D numerical computations

Pure and Applied Geophysics. 2015. Vol. 172. No. 3-4. P. 885-899.
Pelinovsky E., Rybkin A., Nicolsky D., Harris M.
Abstract—Long nonlinear wave runup on the coasts of trapezoidal bays is studied analytically in the framework of one-dimensional (1-D) nonlinear shallow-water theory with crosssection averaging, and is also studied numerically within a twodimensional (2-D) nonlinear shallow water theory. In the 1-D theory, it is assumed that the trapezoidal cross-section channel is inclined linearly to the horizon, and that the wave flow is uniform in the cross-section. As a result, 1-D nonlinear shallow-water equations are reduced to a linear, semi-axis variable-coefficient 1-D wave equation by using the generalized Carrier–Greenspan transformation [CARRIER and GREENSPAN recently developed for arbitrary cross-section channels, and all characteristics of the wave field can be expressed by implicit formulas. For detailed computations of the long wave runup process, a robust and effective finite difference scheme is applied. The numerical method is verified on a known analytical solution for wave runup on the coasts of an inclined parabolic bay. The predictions of the 1-D model are compared with results of direct numerical simulations of inundations caused by tsunamis in narrow bays with real bathymetries