Analytical solution of run-up for non-breaking long waves over bathymetry with arbitrary topography

摘要

The purpose of this study is to extract an analytical formula to determine the maximum amplitudernof non-breaking periodic and solitary long waves at the shoreline with an arbitrary coastalrntopography where it could be considered as run-up. At first, the linear shallow water wavernequations for an arbitrary topography is extracted and then, by using the Maclaurin series of therncoastal topography and with the help of the Frobenius method in solving the differential equations,rnthe wave run-up for the generalized coastal topography is obtained analytically. Finally, to verifyrnthe extracted formula, the simplified formula for simple slope beaches has been compared with itsrnpreviously solved Bessel form formula. In the case of quadratic-form beach topography, the seriesrnsolution was compared with the numerical results of wave run-up as well.