EFFECTS OF DENSITY OF INUNDATION WATER ON TSUNAMI RUN-UP

Abstract

 Aiming for the advancement of historical and 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 with sediment over a uniformly sloping bottom under the condition that the friction factor K is not linked to the density ρ of inundation water and analytical solutions to a(t), U, d²a/dt², the maximum run-up distance a_m and height R_m under the condition that K is linked to ρ are derived, and effects of ρ 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 R_m can be predicted accurately, there is a possibility of evaluating the run-up duration time inaccurately and vice versa, and (2) linking K to ρ is necessary to solve this matter. An expression for the relationship between K and ρ is also presented. Moreover, it is verified that the derived series and analytical solutions are useful to discuss the effects of ρ on the run-up of tsunami with sediment through a comparison between the experimental and theoretical maximum run-up distances.