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.
|Commitee:||Nikolsky, Dmitry, Williams, Gordon|
|School:||University of Alaska Fairbanks|
|Department:||Mathematics and Statistics|
|School Location:||United States -- Alaska|
|Source:||MAI 55/01M(E), Masters Abstracts International|
|Subjects:||Applied Mathematics, Geophysics, Mathematics|
|Keywords:||Carrier–Greenspan transformation, Finite difference method, Long wave run-up, Numerical simulation, Shallow water wave equations, Spectral solution|
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