Numerical realization of the generalized Carrier-Greenspan transform for the shallow water wave equations |
Posted on:2016-10-14 | Degree:M.S | Type:Thesis |
University:University of Alaska Fairbanks | Candidate:Harris, Matthew W | Full Text:PDF |
GTID:2470390017481926 | Subject:Applied Mathematics |
Abstract/Summary: | |
Run-up of long waves in sloping U-shaped bays is studied analytically in the framework of the 1-D nonlinear shallow-water theory. By assuming that the wave flow is uniform along the cross-section, 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 (Rybkin et al., 2014). A spectral solution is developed by solving the linear semiaxis variable-coefficient 1-D equation via separation of variables and then applying the inverse Carrier-Greenspan transform. To compute the run-up of a given long wave a numerical method is developed to find the eigenfunction decomposition required for the spectral solution in the linearized system. The run-up of a long wave in a bathymetry characteristic of a narrow canyon is then examined. |
Keywords/Search Tags: | Wave, 1-D, Carrier-greenspan |
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