AbstractAiming for the advancement of historical and/or prospective tsunami scale evaluations, and focusing on the tsunami run-up, series solutions to the tip position a(t), velocity U (=da/dt) and acceleration d2a/dt2 in the tip region of inundation flow (unsteady flow) with sediment over a uniformly sloping bottom under the condition that the friction factor K is not linked to the density of inundation water, and analytical solutions to a(t), U(t), d2a/dt2, the maximum run-up distance a_m and height Rm under the condition that K is linked to density are derived, and effects of density on them and run-up process are theoretically examined. It is indicated that (1) in the run-up analysis (including numerical simulation) of tsunami with sediment under the condition of a constant K, even if a_m and Rm can be predicted accurately, there is a possibility of evaluating the run-up duration time inaccurately and vice versa, and (2) linking K to density is necessary to solve this matter. An expression for the relationship between K and is also presented. Moreover, it is verified that the derived series and analytical solutions are useful to discuss the effects of density on the run-up of tsunami with sediment through a comparison between the experimental and theoretical maximum run-up distances.
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