EFFECT OF THE DENSITY OF INUNDATION WATER ON TSUNAMI RUN-UP

Hideo Matsutomi

doi:10.9753/icce.v36v.papers.62

Abstract

Aiming 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.

Highlights

Aiming for the advancement of the tsunami load, and historical and/or prospective tsunami scale evaluations, the dependency of the density ρ of inundation water on hydraulic quantities such as incident Froude number Fri, and the dependencies of the maximum tsunami run-up distance, sediment deposit distance, etc. on ρ were examined through a small-scale hydraulic experiment (Matsutomi and Konno 2019)
It can be seen through a comparison with the results shown in Figure 3, which are obtained by adopting the friction factor K having a constant value averaged over the whole process of run-up and backwash of inundation flow, that the results shown in Figure 8 indicate the run-up duration time becomes short for the maximum run-up distance am
Main results obtained by this study are that: 1. Series solutions to the tip position a(t) (Equations (26) and (29)), velocity U (=da/dt) and acceleration d2a/dt2 in the tip region of inundation flow with sediment on a movable bed uniformly sloped under the condition that the friction factor K was not linked to the density ρ of inundation water, and analytical solutions to a(t) (Equation (45)), U(t) (Equation (46)), d2a/dt2 (Equation (47)), the maximum run-up distance am and height Rm (Equation (49)) under the condition that K was linked to ρ were derived, and effects of ρ on them and run-up process were examined (Figures 3 to 12)

Summary

INTRODUCTION

Aiming for the advancement of the tsunami load, and historical and/or prospective tsunami scale evaluations, the dependency of the density ρ of inundation water on hydraulic quantities such as incident Froude number Fri, and the dependencies of the maximum tsunami run-up distance, sediment deposit distance, etc. on ρ were examined through a small-scale hydraulic experiment (Matsutomi and Konno 2019). In this study, focusing on the tsunami run-up, solutions to the tip position a(t), velocity U(t), run-up height Rm and so on of inundation flow (unsteady flow) with sediment over a uniformly sloping bottom are derived theoretically, effects of ρ on them and run-up process of inundation flow are examined, and knowledge concerning them is enhanced as a result. The conservation law of mass M in the tip region of inundation flow with the bottom friction (or sediment) could be expressed as follows (refer to Matsutomi 1985): dM dt xs d(. When K is a friction factor of inundation flow on a movable bed (Matsutomi 2019), the conservation law of momentum P in the tip region of inundation flow could be expressed as follows: dP dt

Ud dt xs

Findings

CONCLUSIONS