2023 Volume 79 Issue 17 Article ID: 23-17027
Aiming for the advancement of evaluation of wave force due to tsunami inundation flow, a theory for evaluating water surface profile in the tip region of tsunami inundation flow with sediment over a uniformly sloping movable bed, which is based on a simple tsunami inundation flow model reported previously, is proposed including the cases using only mass conservation law and using only momentum conservation law. It is indicated that the water surface profile in the case using both mass and momentum conservation laws is expressed by the complementary error function and as the specific gravity of inundation water becomes greater, the water surface gradient and therefore wave force increases. A theory for evaluating volume of bed material movement and average depth of bed scour in the tip region of tsunami inundation flow, which is based on the same tsunami inundation flow model, is also proposed. It is indicated that both the volume of bed material movement and the average depth of bed scour monotonically increase with time. Except for the early and the final stages in the inundation process, validity of the proposed theories is also confirmed through a comparison between existing experimental values obtaind under a condition of horizontal bed composed of sand and theoretical values on the water surface profile and the average depth of bed scour in the tip region of inundation flow.
