Abstract
We analytically solve the nonlinear shallow water theory for the tsunami run-up on a plane beach in the presence of tide and show that over a plane beach the tide in the nearshore zone can be considered static (uniform in space and frozen in time). With this assumption, we find an exact analytical solution for the tsunami run-up height as a function of the amplitude of the incident wave and analyse the influence of the tide on the tsunami run-up characteristics. We confirm these results by calculation of the total tsunami and tidal run-up field using analytical solutions of the initial nonlinear shallow water equations.
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