Three-dimensional experiments on landslide generated waves at a sloping coast

This paper describes new three dimensional experiments on water waves generated by landslides. The landslide is reproduced by a rigid elliptical body, sliding along an inclined plane (slope of 1/3, 1 vertical, 3 horizontal). The generated water waves are free to propagate both offshore and alongshore, since the plan dimensions of the used wave tank are of at least one order of magnitude larger than the width of the landslide, which can be considered to be a scale of the wave length. The experimental study has been carried out reproducing both subaerial and partially submerged landslides. The wave generation process is studied by means of video records of the near field flow and measurement of the landslide movement; the properties of the waves propagating along the coast are described on the basis of runup gauges. The waves observed during the experiments always present first a crest and then a trough; as the first wave propagates away from the generation area the crest tends to become smaller than the trough and the maximum runup along the coast is given by the second or by the third wave. An important feature is that the observed runup along the coast firstly grows with the distance from the generation area, it reaches a maximum value at about two times the width of the landslide, and then decreases. An estimate of the celerity at which the waves propagate along the coast is given on the basis of gauge measurements; it results that the crests propagate faster than the troughs, and the wave period increases.     

Wave types of landslide generated impulse waves

Subaerial landslide generated impulse waves were investigated in a prismatic wave channel. Seven governing parameters, namely the still water depth, slide impact velocity, slide thickness, bulk slide volume, bulk slide density, slide impact angle, and grain diameter, were systematically varied. The generated impulse waves are nonlinear, intermediate- to shallow-water waves involving a small to considerable fluid mass transport. The Stokes wave, cnoidal wave, solitary wave, and bore theories were applied to describe the observed maximum waves. The theoretical and observed features of these four wave types are highlighted. A diagram allows to predict the wave type directly as a function of the slide parameters, the slide impact angle, and the still water depth.     

Laboratory investigations on impulsive waves caused by underwater landslide

Laboratory investigations have been performed on the submarine landslide generated waves by performing 120 laboratory tests. Both rigid and deforming-slide masses are considered. The effects of bed slope angle, initial submergence, slide geometry, shape and deformation on impulse wave characteristics have been inspected. Impulse wave amplitude, period, energy and nonlinearity are studied in this work. The effects of bed slope angle on energy conversion from slide into wave are also investigated. Laboratory-based prediction equations are presented for impulse wave amplitude and period in near and far-field and are successfully verified using the available data in previous laboratory and numerical works.     

Mathematical modelling of a potential tsunami associated with a late glacial submarine landslide in the Sea of Marmara

Potential tsunami waves were modelled on the basis of the morphology and geological setting of a late glacial submarine landslide localized in the north-eastern sector of the Sea of Marmara, using a three-dimensional algorithm with the purpose of assessing the future risk of tsunamogenic landslides in the region. The landslide occurred off the Tuzla Peninsula on the north-eastern slope of the Ç?narc?k Basin, the easternmost of the three deep Marmara basins. The mass movement appears to be related to the Main Marmara Fault that passes below the toe of the failed mass. Observations from earlier manned submersible dives suggest that the initiation of the slide was facilitated by secondary faults associated with the Hercynian orogeny and involved Palaeozoic shales dipping southwards towards the deep basin. Radiocarbon dating of core material, together with the well-dated Marmara sapropel above the chaotically mixed landslide surface, reveal that the latest landslide event occurred about 17 ¹⁴C ka b.p. The uppermost scar of the landslide is found at 250 m and its toe at about 1,200 m below the present sea level. At the time of the slide, the Marmara Sea Basin was lacustrine, with its water level at ?85 m. In plan view the landslide has a distinctively triangular shape and the lateral extent of its toe is about 10 km. Multibeam bathymetric data indicate that the sliding motion probably occurred in two phases: a slower phase affecting the eastern part, characterized by an undulating surface, and a more rapid phase affecting the western part that possibly created tsunami waves. In the seismic sections, older failed slide masses can be clearly identified; these were probably displaced during marine isotopic stage 6 (～127–160 ka b.p.). The front of this buried material is located more than 1.5 km further south of the fault. We used a three-dimensional, Green’s function-based potential theory approach, rather than shallow-water equations commonly used in conventional tsunami simulations. The solution algorithm is based on a source-sink formulation and an integral equation. The results indicate that the maximum height of the tsunami in the Ç?narc?k Basin could have reached about half the average thickness of the sliding mass over a lateral extent of 7 km. Assuming an average thickness of 30 m for the landslide, and considering that the water level at 17 ka b.p. was at about ?85 m, the modelling shows that the maximum wave height generated by the slide would have been about 15–17 m.     

Sediment grains moved by passing tsunami waves: Tsunami deposits in deep water

Tsunamis propagating in the open ocean have associated horizontal particle velocities that do not change with depth — yet the limiting water depth where a tsunami of given characteristics will initiate sediment motion remains unknown. Based upon linear wave theory and a parametrization of the Shields curve, equations are derived and solved, using an iterative scheme, to address the topic of grain movement by tsunami waves as a function of water depth and wave amplitude. The focus is on waves in deep water where tsunami waves behave linearly and on non-cohesive sediment grains. Furthermore, the question is addressed of which grain sizes are picked up on a sloping beach as the wave shoals. According to the results, even the Boxing Day tsunami in 2004 was incapable of moving fine sand in water deeper than 985 m in the Bay of Bengal and 335 m in the Indian and Pacific oceans. The results suggest that tectonic tsunamis of size equal to or smaller than the Boxing Day tsunami cannot initiate motion of deep-water cohesionless sediments that can be correlated on an oceanic basin-wide scale.     

Numerical simulation of waves generated by landslides using a multiple-fluid Navier–Stokes model

This work reports on the application and experimental validation, for idealized geometries, of a multiple-fluid Navier–Stokes model of waves generated by rigid and deforming slides, with the purpose of improving predictive simulations of landslide tsunamis. In such simulations, the computational domain is divided into water, air, and slide regions, all treated as Newtonian fluids. For rigid slides, a penalty method allows for parts of the fluid domain to behave as a solid. With the latter method, the coupling between a rigid slide and water is implicitly computed (rather than specifying a known slide kinematics). Two different Volume of Fluid algorithms are tested for tracking interfaces between actual fluid regions. The simulated kinematics of a semi-elliptical block, moving down a water covered plane slope, is first compared to an earlier analytical solution. Results for the vertical fall of a rectangular block in water are then compared to earlier experimental results. Finally, more realistic simulations of two- and three-dimensional wedges sliding down an incline are compared to earlier experiments. Overall, in all cases, solid block velocities and free surface deformations are accurately reproduced in the model, provided that a sufficiently resolved discretization is used. The potential of the model is then illustrated on more complex scenarios involving waves caused by multi-block or deformable slides.     

Scenarios of local tsunamis in the China Seas by Boussinesq model

The Okinawa Trench in the East China Sea and the Manila Trench in the South China Sea are considered to be the regions with high risk of potential tsunamis induced by submarine earthquakes. Tsunami waves will impact the southeast coast of China if tsunamis occur in these areas. In this paper, the horizontal two-dimensional Boussinesq model is used to simulate tsunami generation, propagation, and runnp in a domain with complex geometrical boundaries. The temporary varying bottom boundary condition is adopted to describe the initial tsunami waves motivated by the submarine faults. The Indian Ocean tsunami is simulated by the numerical model as a validation case. The time series of water elevation and runup on the beach are compared with the measured data from field survey. The agreements indicate that the Boussinesq model can be used to simulate tsunamis and predict the waveform and runup. Then, the hypothetical tsunamis in the Okinawa Trench and the Manila Trench are simulated by the numerical model. The arrival time and maximum wave height near coastal cities are predicted by the model. It turns out that the leading depression N-wave occurs when the tsunami propagates in the continental shelf from the Okinawa Trench. The scenarios of the tsunami in the Manila Trench demonstrate significant effects on the coastal area around the South China Sea.     

Numerical Modeling of Sediment Mass Sliding and Tsunami Generation: The Case of February 7, 1963, in Corinth Gulf,Greece

Numerical modeling of a landslide process at the continental slope by taking into account slope parameters is performed for the tsunami event of February 7, 1963, reported in the Corinth Gulf, central Greece. A layered sediment structure was considered, and an initial external dynamic action at the landslide process was introduced. The results obtained were quite consistent with the observational runup data as well as with the results arrived at by conventional rigid-body and viscous-fluid models. However, this approach permits to describe in detail the formation of several wave groups and particular tsunami characteristics that are strongly dependent on the landslide model.     

Numerical Modeling of Sediment Mass Sliding and Tsunami Generation: The Case of February 7, 1963, in Corinth Gulf, Greece

Numerical modeling of a landslide process at the continental slope by taking into account slope parameters is performed for the tsunami event of February 7, 1963, reported in the Corinth Gulf, central Greece. A layered sediment structure was considered, and an initial external dynamic action at the landslide process was introduced. The results obtained were quite consistent with the observational runup data as well as with the results arrived at by conventional rigid-body and viscous-fluid models. However, this approach permits to describe in detail the formation of several wave groups and particular tsunami characteristics that are strongly dependent on the landslide model.     

The effects of variable speeds of a submarine block slide on near-field tsunami amplitudes

In this study, the motion of a submarine block slide, with variable velocities, and its effects on the near-field tsunami amplitudes are investigated. The numerical results show that the amplitudes generated by the slide are almost the same as those created by its average velocity when , where is average velocity of the slide and is the long period tsunami velocity in ocean of constant depth h. In contrast, the kinematic model of the slide must take into account time variations in the moving velocity, if , especially when .     

Numerical investigation of tsunami-like wave hydrodynamic characteristics and its comparison with solitary wave

Solitary waves have been commonly used as an initial condition in the experimental and numerical modelling of tsunamis for decades. However, the main component of a tsunami waves acts at completely different spatial and temporal scales than solitary waves. Thus, use of solitary waves as approximation of a tsunami wave may not yield realistic model results, especially in the coastal region where the shoaling effect restrains the development of the tsunami wave. Alternatively, N-shaped waves may be used to give a more realistic approximation of the tsunami wave profile. Based on the superposition of the sech²(*) waves, the observed tsunami wave profile could be approximated with the N-shaped wave method, and this paper presents numerical simulation results based on the tsunami-like wave generated based on the observed tsunami wave profile measured in the Tohoku tsunami. This tsunami-like wave was numerically generated with an internal wave source method based on the two-phase incompressible flow model with a Volume of Fluid (VOF) method to capture the free surface, and a finite volume scheme was used to solve all the governing equations. The model is first validated for the case of a solitary wave propagating within a straight channel, by comparing its analytical solutions to model results. Further, model comparisons between the solitary and tsunami-like wave are then made for (a) the simulation of wave run-up on shore and (b) wave transport over breakwater. Comparisons show that use of these largely different waveform shapes as inputs produces significant differences in overall wave evolution, hydrodynamic load characteristics as well as velocity and vortex fields. Further, it was found that the solitary wave uses underestimated the total energy and hence underestimated the run-up distance.     

Revisiting the February 6th 1783 Scilla (Calabria, Italy) landslide and tsunami by numerical simulation

On February 6th, 1783, a landslide of about 5 × 10⁶ m³ triggered by a 5.8 M earthquake occurred near the village of Scilla (Southern Calabria, Italy). The rock mass fell into the sea as a rock avalanche, producing a tsunami with a run-up as high as 16 m. The tsunami killed about 1,500 people, making it one of the most catastrophic tsunamis in Italian history. A combined landslide-tsunami simulation is proposed in this paper. It is based on an already performed reconstruction of the landslide, derived from subaerial and submarine investigation by means of geomorphological, geological and geomechanical surveys. The DAN3D model is used to simulate the landslide propagation both in the subaerial and in the submerged parts of the slope, while a simple linear shallow water model is applied for both tsunami generation and propagation. A satisfying back-analysis of the landslide propagation has been achieved in terms of run-out, areal distribution and thickness of the final deposit. Moreover, landslide velocities comparable to similar events reported in the literature are achieved. Output data from numerical simulation of the landslide are used as input parameters for tsunami modelling. It is worth noting that locations affected by recordable waves according to the simulation correspond to those ones recorded by historical documents. With regard to run-up heights a good agreement is achieved at some locations (Messina, Catona, Punta del Faro) between computed and real values, while in other places modelled heights are overestimated. The discrepancies, which were most significant at locations characterized by a very low slope gradient in the vicinity of the landslide, were probably caused by effects such as wave breaking, for which the adopted tsunami model does not account, as well as by uncertainties in the historical data.     

Experiments on slide generated waves in a 1:500 scale fjord model

An unstable rock-slope is detected in Åkerneset, located in Storfjorden, Western Norway. In the future this rock-slope will produce a slide and a subsequent tsunami. In accordance to this future event, experiments in a 1:500 scale model of the inner part of Storfjorden are performed, where the model geometry is made after the real fjord bathymetry, while the slide is an idealized slide of block-type. The slide motion is monitored and the generated waves are measured at a number of wave gauges in the model. At selected locations local details of the flow, velocities and inundation are measured by digital image techniques and acoustic probes. Features of the wave system and the inundation are elaborately discussed with a view to the future event as well as to the application of models.     

Tsunami simulation with Green–Naghdi theory

Green–Naghdi (GN) theory is a fully nonlinear wave theory which has been used with success to simulate nonlinear water waves. In previous applications of GN theory to water wave problems the ocean bottom was assumed to be time invariant. In this work no such restriction is made and GN theory is used to simulate tsunami caused by bottom fluctuation. As first test cases we simulate two-dimensional nonlinear surface waves generated by positive bottom movements. The results in the generation region for three different seabed movements compare well against earlier experimental data. The results in the downstream region for impulsive seabed movements show some discrepancies in wave phase and amplitude compared with earlier experimental values. It is suspected that the viscous effects may have played a role. The GN theory is then used to study three-dimensional near-field tsunami amplitudes caused by submarine landslides and slumps spreading in two orthogonal directions. The GN results agree with previous linear solution very well when the ratio of the velocities is v₁/v₂=1.0. But GN theory give more believable results for the case of v_T/v=0.1 and v₁/v₂=0.1.     

Fluidization Process in Submarine Landslides: Physical and Numerical Considerations

Fluidization processes in submarine landslides were studied by physical and numerical means. To examine soil-water interactions in the fluidization process, the computer axial tomography (CAT)-scan imaging techniques and laboratory vanes were utilized with a focus on the transition from failure to post-failure. Based on the results that were obtained from the scanning images and laboratory vane tests after the process of water infiltration into the soil sample, it appears that a gradual decrease in shear strength is unavoidable with increasing water content in a shear zone. From the numerical results, which were based on the dam-break problem using the transport equation coupled with the Navier-Stokes equation, if the slide is assumed to be initially unstable, a possible transition of fluidization processes that are dependent upon a change in density occurs. The density of the mud decreases with time during the flow at the interface between mud and water. The upper part of the mud pushes the lower part of the mud and then induces a rotation of mud that moves substantial distances. These results emphasize the importance of the soil-water interaction, the need for sediment rheology and the influence of the water circulation on the motion of the landslide.     

实验室造波条件对内孤立波发展影响的直接数值模拟

内孤立波具有振幅尺度大、能量集中的特点,其引起流场和密度场的迅速变化可能对海洋工程结构物以及水下潜体造成严重威胁。因此研究不同造波条件下生成的内孤立波运动的流场特征具有重要的学术意义和实际应用价值。采用直接数值模拟方法和给定的初始密度场密度跃迁函数,对重力塌陷激发内孤立波的运动过程进行研究,探讨了不同造波条件下,激发产生的内孤立波波型、涡度、振幅和水平速度等流场特征。结果表明:(1)直接模拟数值方法能够模拟内孤立波传播过程中的密度界面波型反转现象;(2)从定性和定量的角度,证实了不稳定内孤立波传播过程中存在能量的向后传递;(3)对于相同的台阶深度(水闸两侧初始密度界面的高度差),初始涡流保持相同,但是随着上下层水深比的减小,其强度下降显著;(4)台阶深度对初始涡流的垂直结构的影响要大于上下层水深比,且台阶深度对内孤立波的振幅、水平速度的影响显著。     

A mathematical model of calculating local tsunami wave source constraints and propagation

This paper presents a local tsunami simulation, including the initial displacement field model of tsunami source and tsunami wave propagation model. We deduced the tsunami wave equation; applied the ma...     

Numerical simulation of the tsunami generated by a past catastrophic landslide on the volcanic island of Ischia, Italy

The island of Ischia, Gulf of Naples, Italy, like many other volcanic islands is affected by mass failures, that are mainly related to secondary volcanic processes such as slope steepening and seismic shaking. The block resurgence of its main relief, Mount Epomeo, has been recognised to contribute cyclically to mass instability and cause landslides, that occasionally may reach the sea and start tsunamis. In this work we explore the consequences of the Ischia Debris Avalanche (IDA), a flank collapse that occurred in historical times, and involved the whole Mount Epomeo edifice including its submarine portion, and that may have caused gigantic sea waves affecting all the coasts of Ischia and of the Gulf of Naples. The IDA and the generated tsunami have been taken as the worst-case scenario for the occurrence of a new tsunami in the area. They have been simulated through numerical codes developed and maintained by the University of Bologna. The simulation shows that the IDA-induced tsunami attacks severely all the coasts of the Gulf of Naples with the highest waves obtained for the island of Ischia, the island of Capri and the peninsula of Sorrento. The propagation pattern of the IDA tsunami can be used to get hints on the impact that such an event may have had on early populations habiting Gulf of Naples, but also to get clues on the area that could be most severely hit by a tsunami generated by a smaller-scale landslide that may occur in the same source zone.     

Wave dispersion study for tsunami propagation in the Sea of Marmara

In this paper the aim is to investigate whether there are differences between the dispersion and non-dispersion solutions on tsunami propagation. For this purpose, two numerical models of tsunami propagation are compared. One of these numerical models is a nondispersive model that uses Saint Venant equations and the other is a dispersive model that uses Boussinesq equations. The tsunamis resulting from a submarine mass failure (SMF) which is settled at the bottom of the north eastern Sea of Marmara are examined. An analytical solution considering wave dispersion is developed for obtaining near-field tsunami amplitudes above the submarine mass failure. Numerical modeling is used at the sea surface from the common boundary called as liquid boundary with incident waves up to the coastal regions to get the tsunami amplitudes. The output of the analytical model is taken as the disturbances for the numerical method. In the numerical solutions TELEMAC-2D software system is used for both dispersive and nondispersive modeling. The results of the dispersive and nondispersive models are compared to each other. Both temporal and spatial differences in the amplitudes and wave shapes are examined. The obtained results demonstrate that there are no noticeable differences between the dispersion and non-dispersion solutions except some special cases and some special landslide velocities.     

南海北部神狐海域海底滑坡在地震剖面上的识别及形成机制

海底滑坡广泛发育于海底陆坡,是沉积物往深海盆地搬运的重要方式。大规模的突发性海底滑坡事件不但可以改变海底地形地貌,还可能触发海啸,给沿海地区居民的生命和财产带来巨大损失。对海底滑坡地震响应特征进行研究,可以推断其物质来源、形成机制以及演化模式,为人类的防灾减灾提供科学依据。神狐海域地处被动大陆边缘,海底构造复杂,大陆坡较陡,具有发育海底滑坡的条件。结合最新采集的三维地震数据,在南海北部神狐海域发现了多期海底滑坡,研究表明,这些海底滑坡在地形上具有以下特征:在坡度剧烈变化处,有弧形主陡坎,沿着主要陡坎的两侧向下延伸则会出现近平行的侧壁,在海底峡谷侧壁和在较顺直的海底斜坡上存在圈椅状陡坎或陡壁。在对研究区海底滑坡的地震响应特征分析的基础上,研究了海底滑坡的地貌特征、内部结构及几何形态,探讨了南海北部陆坡神狐海域海底滑坡的形成机制,对于开展区域海洋工程,防止灾害发生具有重要意义。