Modeling of breaking solitary wave run up

TLDR: In this article, a series of laboratory experiments measuring the non-breaking and breaking solitary wave run up along with analytical solution for a solitary wave propagating over constant depth and then running up a sloping beach.

Abstract: The Aceh tsunami in 2004 and also the tsunami on the north east coast of Japan recently clearly showed the massive impact of tsunami waves to coastal area. The tsunami wave carries and transports large amount of sediment, resulting in coastal morphology changes. It is very important to understand the tsunami wave in order to reduce and to minimize the damage. Thus, tsunami modeling study is important to assess the impact of a tsunam i wave on coastal area. Tsunami modeling has been studied widely, by means of laboratory experiment, analytical solution , and numerical simulation. One of the studies that are considered to have significant impact on the field is canonical problems . The study covered a series of laboratory experiments measuring the non-breaking and breaking solitary wave run up along with analytical solution for a solitary wave propagating over constant depth and then running up a sloping beach. The study also contributes to numerical study by providing data set for model verification and validation. Various models have been developed with various methods and approaches. Simplified approaches are often used for practical application . Simplified approach such as found in depth averaged SWE model has been widely used for numerical simulation of solitary wave run up and is known to yield tsunami evolution well . Titov and Synolakis have used SWE model to compute a range of real tsunami inundation, including the 199 3 Okushiri tsunami. Realization of breaking wave in SWE model is still a challenge since it has no appropriate term for breaking wave simulation. Other governing equation, such as Boussinesq-type , can adopt breaking wave treatment by introducing a constant value of eddy viscosity in the shallower area . However, this odel requires longer computation time and does not easily adapt wetting and drying (moving boundary) treatments as compare to the SWE model. It is also noted that their performance and accurac y for tsunami run up even for landslide wave does not xceed SWE model . Advanced computational method provides a more realistic way to simulate breaking wave. One of the leading method is Volume of Fluid Method, i.e., NEWFLUME . Nevertheless, these methods include more terms and far more complex than the SWE. Certain treatments and numerical schemes can be applied to SWE model in order to achieve stability and accuracy for wave breaking simulation . The Mac Cormack scheme had been widely employed to solve SWE for investigating run up of a uniform bore on a sloping beach . Nevertheless, volume conservation problem arises due to discontinuities. Steep gradients of conservative terms may cause numerical error, which can be 土木学会論文集 B3(海洋開発) Vol.67,No.2,2011