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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,they made a lot of simplifications,and did not consider the effects of Coriolis force and bottom friction on tidal wave.In this paper,the first-order linear mild-slope equations are deduced from Kirby mild-slope equation including wave and current interaction.Then,referring to the method of wave equations’ modification,the Coriolis force and bottom friction term are considered,and the effects of which have been performed with the radial sand ridges topography.Finally,the results show that the modified mild-slope equation can be used to simulate tidal motion,and the calculations agree well with the measurements,thus the applicability and validity of the mild-slope equation on tidal simulation are further proved.
Since the mild-slope equation was derived by Berkhoff (1972), the researchers considered various mechanisms 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, they made a lot of simplifications, and did not consider the effects of Coriolis force and bottom friction on tidal waves. In this paper, the first-order linear mild-slope equations are deduced from Kirby mild-slope equations including wave and current interaction. Chen, referring to the method of wave equations’ modification, the Coriolis force and bottom friction term are considered, and the effects of which have been performed with the radial sand ridges topography. Finally, the results show that the modified mild-slope equation can be used to simulate tidal motion, and the calculations agree well with the the measurements, thus the applicability and validity of the mild-slope equation on tidal simulation are further proved.