Three-dimensional sediment transport processes on tsunami-induced topography changes in a harbor
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2012
Received: 26 October 2010
Accepted: 30 May 2011
Published: 24 October 2012
A three-dimensional hydrostatic numerical simulation on tsunami-induced topography changes near a harbor is carried out, and sediment transport processes on a significant local deposition near the center of the harbor caused by a tsunami, which was observed in an early experimental study, are investigated. This local deposition has not been well predicted by a vertically averaged hydrodynamic model. The results show that velocities, water levels and topography changes in the harbor predicted in this study agree with the experimental data. The local deposition has relations with a vortex generated in the harbor when the tsunami attacks the harbor. At areas near the vortex center, a secondary flow of the first kind develops, and it plays the role of transporting suspended sediment to the vortex center, located near the center of the harbor, and causes the local deposition there. In order to predict deposition areas with high accuracy, the secondary flow effects should be incorporated in prediction methods of tsunami-induced topography change. Key words: Tsunami, tsunami deposits, sediment transport, hydrodynamic model.
Large tsunamis cause extensive sediment transport in coastal areas. In the past two decades, the tsunami-induced topography changes and the sediment deposition (tsunami deposits), which result from tsunami-induced sediment transport, have become a matter of interest to many geologists and engineers because they are related to tsunami risks (e.g., Dawson and Shi, 2000; Moore et al., 2006; Dawson and Stewart, 2007). A large tsunami transports seabed sediment over large areas and creates deposition of continuous and discontinuous sediment sheets across large areas of the coastal zone (e.g., Hindson etal., 1996; Dawson and Shi, 2000). Thus, tsunami deposits are of geological interest as evidence for the occurrence of past tsunamis and for estimating past tsunami inundation areas. On the other hand, tsunami-induced sediment transport in coastal zones causes local scouring and deposition around coastal facilities. Tomita et al. (2006) reported that extensive erosion was observed around coastal structures and piers in southwest Sri Lanka after the 2004 Indian Ocean tsunami, and as a result their functions and abilities were lost even though damage to the structures themselves was not observed. Thus, tsunami-induced topography changes are of engineering interest that they may adversely affect the ability of coastal facilities.
Tsunamis cause different topography changes than storms in coastal zones because of their different driving forces. Tsunamis have long wavelengths and long wave periods 10 min–1 hour. Thus, tsunami inundation areas are wide and tsunami-induced topography changes occur over larger areas than those caused by wind waves. Furthermore, seabed sediment experiences strong shear stress continuously for a longer time than in the case of wind waves, resulting in tsunami-induced topography changes having different features from storm-induced topography changes.
Numerical models of tsunami-induced topography changes have been developed in a decade (Takahashi et al., 2000; Nishihata et al., 2006; Jaffe and Gelfenbuam, 2007; Huntington et al., 2007; Fujii et al., 2009; Gusman et al., 2010; Huang et al., 2010; Apotsos et al., 2011). These models are classified into two types; inverse models and forward models (Huntington et al., 2007). The inverse models are used to calculate tsunami flow speed from distributions of tsunami deposits. Jaffe and Gelfenbuam (2007) applied an inverse model to a prediction of flow speeds using field data collected at Arop, Papua New Guinea, after the 1998 tsunami. Their model assumes that tsunami-induced sediment transport is under a steady, spatially uniform process and flow speeds are determined by local thickness and grain size of deposits. They showed agreement with estimation by application of Bernoulli’s principle to water levels on buildings and an inundation model.
In the forward models, inundation areas, tsunami flow speeds, and water depths are calculated by hydrodynamic models, and topography changes are calculated by sediment transport models. Goto et al. (2011) calculated the inundation process of the 2004 Indian Ocean tsunami near Kirinda harbor, Sri Lanka, using a two-dimensional vertically averaged hydrodynamic model, and investigated difference observed in bathymetric data one month before and 2 months after the tsunami. Takahashi et al. (2000) and Nishihata et al. (2006) coupled vertically averaged hydrodynamic models and sediment transport models, and carried out numerical simulations of topography changes in Kesen-numa port due to the 1960 Chilean tsunami and those in Kirinda harbor due to the 2004 Indian Ocean tsunami, respectively. In the vertically averaged models, vertical averaged velocities and suspended sediment concentrations are calculated, and vertical profiles of velocity and suspended sediment concentration are given analytically. On the other hand, Apotsos et al. (2011) and Kihara and Matsuyama (2011) applied three dimensional hydrodynamic models with the hydrostatic assumption to estimations of topography changes in Kuala Meurisi, Sumatra, and Kirinda harbor, Sri Lanka, respectively, due to the 2004 Indian Ocean tsunami. Before applying to the sediment transport simulation, Apotsos et al. (2011) carried out a set of benchmark simulations for tsunami run-up, but not for tsunami-induced sediment transport because no standardized benchmarks exists.
Fujii et al. (2009) carried out an experiment using a wide flume in order to clarify characteristic flow patterns and topography changes in harbors due to a tsunami. In their experiment, topography changes near an idealized harbor due to an isolated long wave were investigated. Furthermore, they also carried out numerical simulations on the tsunami-induced topography changes using a vertically averaged model. Their model encountered a difficulty in predicting deposition areas in the harbor. Although a significant local deposition area was observed at the center of the harbor in their experiment, a widespread deposition area was predicted by their numerical model. This inconsistence may have originated from three-dimensional sediment transport in the deposition processes, which cannot be expressed by the vertically averaged model.
In the present study, in order to investigate the deposition processes at the center of the harbor observed in the experiment of Fujii et al. (2009), a three-dimensional hydrostatic numerical simulation is carried out, and we discuss the roles of the three-dimensional sediment transport in the deposition processes. The idealized experiment of Fujii et al. (2009) is an appropriate benchmark for understanding typical tsunami-induced sediment transport processes in harbors or in inner bays, which are important for both geological and engineering aspects because those will be helpful both for searching historical or pre-historical tsunami deposits in inner bays and for safety assessments of coastal structures. This paper is organized as follows: First, Section 2 describes the numerical model used in this study. Then, Section 3 shows the numerical results and a comparison with experimental data. Furthermore, in Section 3, we attempt to clarify the deposition processes on the basis of the results of the numerical simulation.
2. Numerical Model
2.1 Governing equations for flow
2.2 Sediment transport equations
2.3 Boundary conditions
2.4 Numerical method
In the numerical simulation, the discretized governing equations (2)–(4), (7), and (13) are solved using the finite-difference method on staggered grids. The first-order up wind differential scheme is used for the advection terms and the second-order central differential scheme is used for the other terms. For the time integration of these equations, the free-surface correction method proposed by Chen (2003) is used. In this method, a semi-implicit scheme is used for the time integration of the vertical diffusion terms and terms including the water level, and an explicit scheme is used for the other terms to allow a long time interval.
2.5 Validation of the numerical model
3. Tsunami-Induced Topography Change in a Harbor
In this section, a three-dimensional hydrostatic numerical simulation of the tsunami-induced topography changes studied experimentally by Fujii et al. (2009) is carried out, and the deposition process at the center of the harbor is discussed.
3.1 Experiment of Fujii et al. (2009)
3.2 Numerical conditions
3.3 Numerical results and comparisons with experimental data
The erosion depths near the exterior and interior breakwaters predicted in this study are 1.7 cm and 3.7 cm, and those predicted by the vertically averaged model are 9.4 cm and 5.5 cm, though those observed in the experiment are 5.5 cm and 6.3 cm, respectively. On the other hand, this study predicts local deposition near the center of the harbor, in agreement with the experimental data, whereas the vertically averaged model predicts widespread deposition areas in the harbor as explained in Section 1. This indicates that the local deposition near the center of the harbor may be caused by three-dimensional sediment transport. Note that the deposition height observed in the experiment is 1.3 cm, but those predicted in this study is 0.57 cm and predicted by the vertically averaged model is 0.63 cm, and the both numerical simulations underestimate the deposition height. In the following subsection, the sediment transport processes on the local deposition at the center of the harbor are discussed through the analysis of our numerical results.
3.4 Sediment transport processes on the local deposition at the center of the harbor
At t = 26 s, when the long wave approaches the harbor, a large amount of suspended sediment is generated near the head of the interior breakwater and erosion occurs there (Fig. 11(a)). The suspended sediment is advected in the direction of the flow (Figs. 10(a) and (b)). A high concentration of suspended sediment is observed near the vortex center but the local lowest concentration is observed just at the vortex center at t = 26 s and 36 s. Near the vortex center, which is close to the center of the harbor at t = 36 s, local deposition is observed (Fig. 11(b)). As shown in Fig. 3, the vertically averaged flow in the harbor appears to circulate in the harbor, and thus, the suspended sediment does not tend to be transported toward the vortex center if it is transported along the streamlines of the vertically averaged flow. In the following, we discuss how the suspended sediment is transported toward the vortex center.
Here, we compare strength of the secondary flow observed in this study with those estimated by the method proposed by Kalkwijk and de Vriend (1980) in which strength of secondary flow is guessed by using vertically averaged velocity. The strength of secondary flow A n observed in this study is estimated by assuming that vertical profile of velocity of the secondary flow component is expressed as ǀu c ǀ = A n ǀ f (z)ǀ, where f (z) is a profile function. Using a profile function f (z) = 2(z/h − 1/2) (Odgaard, 1989), A n is calculated by using the cross-components of velocity near the bed shown in Fig. 12.
A three-dimensional hydrostatic numerical simulation on tsunami-induced topography changes near a harbor was carried out, and the deposition processes at the center of the harbor were investigated. The velocity, water level and topography changes in the harbor predicted by our numerical model agree with experimental data. The deposition at the center of the harbor could be predicted by our numerical model, although it could not be well predicted by the vertically averaged numerical model. This is because a secondary flow of the first kind, which was generated near the vortex and developed in the harbor, plays the role of transporting suspended sediment to the vortex center, which is located near the center of the harbor.
Such a vortex has actually been witnessed in harbors after a tsunami (e.g., Okal et al., 2006). Numerical simulations of the topography changes near Kirinda harbor in Sri Lanka induced by the 2004 Indian Ocean tsunami using our numerical model show that some vortices were generated near Kirinda harbor when the tsunami inundated around the harbor, and some deposition areas were observed near the centers of the vortices, in agreement with field survey data (Kihara and Matsuyama, 2011). Thus, to predict deposition areas with high accuracy, the secondary flow effects should be incorporated in numerical models.
The results obtained in this study will be helpful for searching historical or pre-historical tsunami deposits in inner bays. There is a high potential that tsunami deposits are preserved in inner bays where ocean wave influence is weak and thus topography changes due to sediment transports by the ocean waves were little after tsunamis (Fujiwara et al., 2000; Goto et al., 2011). Our results show that depositions induced by tsunamis would be occurred at areas where long-duration sustaining vortices are generated and strong return flows are not occurred. Such vortices would be generated behind peninsulas, which play similar roles to breakwaters in the harbor shown in this study.
We would like to thank Dr. Goto and Dr. Takahashi who gave us invaluable comments and suggestions, which led to significant improvements of our paper.
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