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In the present paper, by introducing the effective wave elevation, we transform the extended elliptic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established...
Since the mild-slope equation was derived by Berkhoff (1972), the researchers considered various mechanism to simplify and improve the equation, which has been widely used for coastal wave field calculation. Recently, some scholars applied the mild-slope equation in simulating the tidal motion, which proves that the equation is capable to calculate the tide in actual terrain. But in their studies,...
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