海啸波作用下泥沙运动——Ⅲ. 数学模型的建立与验证

基于Boussinesq方程耦合泥沙运动和地形演变模型,建立海啸作用下泥沙运动数学模型。地形演变模型采用WENO差分格式,并将WENO差分格式与Lax-Wendroff格式和FTBS格式进行对比分析。运用Synolakis、Kobayashi和Young的实验数据分别对水动力模块和地形演变模块进行验证,数值模拟结果与实验数据吻合良好,模型能够很好地模拟海啸波的传播、破碎、上爬、回落过程以及岸滩的冲淤变化过程,该数学模型能够运用到海啸作用下的岸滩演变研究和预测中。     

Modelling December 2004 Indian Ocean tsunami: a coastal study

December 2004 tsunami in the Indian Ocean region has been simulated using MIKE-21 HD model. The vertical displacement of the seabed is incorporated into the numerical simulation by using time-varying bathymetry data. In the open ocean, sea surface height from altimeter observation has been used to validate the model results. To the west of the rupture zone, the crest is observed to precede the trough of the tsunami waves while to the east, trough preceded the crest. The model performance along the coastal region has been validated using de-tided sea levels from tide gauge measurements at Tuticorin, Chennai, Vishakapattanam, and Paradip ports along the east coast of India. Unique coastal characteristics of the tsunami waves, wave height, and wave celerity are reasonably simulated by the numerical model. Spectral analysis of tide gauge observations and corresponding model results has been done, and the distribution of frequency peaks from the analysis of gauge observations and the model results is observed to have a reasonable comparison. Low-frequency waves, contributed from the coastally trapped edge waves, are found to dominate both the tide gauge observations and the model results. The subsequent increase in the tsunami wave height observed at Chennai, Vishakapattanam, and Paradip has been explained on the basis of coastally trapped edge waves. From the validation studies using altimeter data and tide gauge data, it is observed that the model can be used effectively to simulate the tsunami wave height in the offshore as well as in the coastal region with satisfying performance.     

海啸波作用下岸滩演变与床沙组成变化研究综述

从海啸波作用下岸滩演变、床沙组成变化、建筑物周围淘刷和数值模拟研究4个方面,总结分析了国内外的研究现状和最新进展,指出可控环境下的实验和数值模拟研究相对较少、床沙组成变化缺乏关注、建筑物周围局部冲刷机理认识不足、缺少多尺度数值模拟计算等是当前研究存在的主要不足。在特大型波浪水槽内开展实验研究、发展多尺度混合数学模型、完善海啸波作用下的泥沙输移计算理论等是未来研究取得突破的关键方向。     

Trapped waves of the 27 November 1945 Makran tsunami: observations and numerical modeling

The 27 November 1945 earthquake in the Makran Subduction Zone triggered a destructive tsunami that has left important problems unresolved. According to the available reports, high waves persisted along the Makran coast and at Karachi for several hours after the arrival of the first wave. Long-duration sea-level oscillations were also reported from Port Victoria, Seychelles. On the other hand, only one high wave was reported from Mumbai. Tide-gauge records of the tsunami from Karachi and Mumbai confirm these reports. While the data from Mumbai shows a single high wave, Karachi data shows that high waves persisted for more than 7 h, with maximum wave height occurring 2.8 h after the arrival of the first wave. In this paper, we analyze the cause of these persistent high waves using a numerical model. The simulation reproduces the observed features reasonably well, particularly the persistent high waves at Karachi and the single high wave at Mumbai. It further reveals that the persistent high waves along the Makran coast and at Karachi were the result of trapping of the tsunami-wave energy on the continental shelf off the Makran coast and that these coastally-trapped edge waves were trapped in the along-shore direction within a ∼300-km stretch of the continental shelf. Sensitivity experiments establish that this along-shore trapping of the tsunami energy is due to variations in the shelf width. In addition, the model simulation indicates that the reported long duration of sea-level oscillations at Port Victoria were mainly due to trapping of the tsunami energy over the large shallow region surrounding the Seychelles archipelago.     

Simulation of the Arabian Sea Tsunami propagation generated due to 1945 Makran Earthquake and its effect on western parts of Gujarat (India)

The 1945 Tsunami generated due to Makran Earthquake in the Arabian Sea was the most devastating tsunami in the history of the Arabian Sea and caused severe damage to property and loss of life. It occurred on 28th November 1945, 21:56 UTC (03:26 IST) with a magnitude of 8.0 (M _w), originating off the Makran Coast of Pakistan in the Arabian Sea. It has impacted as far as Mumbai in India and was noticed up to Karvar Coast, Karnataka. More than 4,000 people were killed as a result of the earthquake and the tsunami. In this paper an attempt is made for a numerical simulation of the tsunami generation from the source, its propagation into the Arabian Sea and its effect on the western coast of India through the use of a numerical model, referred to as Tunami-N2. The present simulation is carried out for a duration of 300 min. It is observed from the results that the simulated arrival time of tsunami waves at the western coast of India is in good agreement with the available data sources. The paper also presents run-up elevation maps prepared using Shuttle Radar Topographic Mission (SRTM) data, showing the possible area of inundation due to various wave heights along different parts of the Gujarat Coast. Thus, these results will be useful in planning the protection measures against inundation due to tsunami and in the implementation of a warning system.     

Impact of the National Tsunami Hazard Mitigation Program on Operations of the Richard H. Hagemeyer Pacific Tsunami Warning Center

The first 7 years of the National Tsunami Hazard Mitigation Program (NTHMP) have had a significant positive impact on operations of the Richard H. Hagemeyer Pacific Tsunami Warning Center (PTWC). As a result of its seismic project, the amount and quality of real-time seismic data flowing into PTWC has increased dramatically, enabling more rapid, accurate, and detailed analyses of seismic events with tsunamigenic potential. Its tsunameter project is now providing real-time tsunameter data from seven strategic locations in the deep ocean to more accurately measure tsunami waves as they propagate from likely source regions toward shorelines at risk. These data have already been used operationally to help evaluate potential tsunami threats. A new type of tsunami run-up gauge has been deployed in Hawaii to more rapidly assess local tsunamis. Lastly, numerical modeling of tsunamis done with support from the NTHMP is beginning to provide tools for real-time tsunami forecasting that should reduce the incidence of unnecessary warnings and provide more accurate forecasts for destructive tsunamis.     

Distribution, origin and transport process of boulders deposited by the 2004 Indian Ocean tsunami at Pakarang Cape, Thailand

The tsunami of 2004 in the Indian Ocean transported thousands of meters-long boulders shoreward at Pakarang Cape, Thailand. We investigated size, position and long axis orientation of 467 boulders at the cape. Most of boulders found at the cape are well rounded, ellipsoid in shape, without sharp broken edges. They were fragments of reef rocks and their sizes were estimated to be < 14m³ (22.7t). The distribution pattern and orientation of long axis of boulders reflect the inundation pattern and behavior of the tsunami waves. It was found that there is no clear evidence indicating monotonous fine/coarse shoreward trends of these boulders along each transect line. On the other hand, the large boulders were deposited repeatedly along the three arcuate lines at the intertidal zone with a spacing of approximately 136m interval. This distribution pattern may suggest that long-lasting oscillatory flows might have repositioned the boulders and separated the big ones from small. No boulders were found on land, indicating that the hydraulic force of the tsunami wave rapidly dissipated on reaching the land due to the higher bottom friction and the presence of a steep slope. We further conducted numerical calculation of tsunami inundation at Pakarang Cape. According to the calculation, the sea receded and the major part of the tidal bench (area with boulders at present) was exposed above the sea surface before the arrival of the first tsunami wave. The first tsunami wave arrived at the cape from west to east at approximately 130min after the tsunami generation, and then inundated inlands. Our calculation shows that tsunami wave was focused around the offshore by a small cove at the reef edge and spread afterwards in a fan-like shape on the tidal bench. The critical wave velocities necessary to move the largest and average-size boulders by sliding can be estimated to be approximately 3.2 and 2.0m/s, respectively. The numerical result indicates that the maximum current velocity of the first tsunami wave was estimated to be from 8 to 15m/s between the reef edge and approximately 500m further offshore. This range is large enough for moving even the largest boulder shoreward. These suggest that the tsunami waves that were directed eastward, struck the reef rocks and coral colonies, originally located on the shallow sea bottom near the reef edge, and detached and transported the boulders shoreward.     

Numerical simulation of erosion and deposition at the Thailand Khao Lak coast during the 2004 Indian Ocean tsunami

A case study was conducted for the Thailand Khao Lak coast using a forward numerical model to understand uncertainties associated with interpreting tsunami deposits and relating them to their tsunami sources. We examined possible effects of the characteristics of tsunami source, multiple waves, sediment supply and local land usages. Numerical results showed that tsunami-deposit extent and thickness could be indicative of the slip value in the source earthquake near the surveyed coastal locations, provided that the sediment supply is unlimited and all the deposits are well preserved. Deposit thickness was found to be largely controlled by the local topography and could be easily modified by backwash flows or subsequent tsunami flows. Between deposit extent and deposit thickness, using deposit extent to interpret the characteristics of a tsunami source is preferable. The changing of land usages between two tsunami events could be another important factor that can significantly alter deposit thickness. There is a need to develop inversion models based on tsunami heights and/or run-up data for studying paleotsunamis.     

Identification of tsunami deposits considering the tsunami waveform: An example of subaqueous tsunami deposits in Holocene shallow bay on southern Boso Peninsula, Central Japan

This study proposes a tsunami depositional model based on observations of emerged Holocene tsunami deposits in outcrops located in eastern Japan. The model is also applicable to the identification of other deposits, such as those laid down by storms. The tsunami deposits described were formed in a small bay of 10–20-m water depth, and are mainly composed of sand and gravel. They show various sedimentary structures, including hummocky cross-stratification (HCS) and inverse and normal grading. Although, individually, the sedimentary structures are similar to those commonly found in storm deposits, the combination of vertical stacking in the tsunami deposits makes a unique pattern. This vertical stacking of internal structures is due to the waveform of the source tsunamis, reflecting: 1) extremely long wavelengths and wave period, and 2) temporal changes of wave sizes from the beginning to end of the tsunamis.

The tsunami deposits display many sub-layers with scoured and graded structures. Each sub-layer, especially in sandy facies, is characterized by HCS and inverse and normal grading that are the result of deposition from prolonged high-energy sediment flows. The vertical stack of sub-layers shows incremental deposition from the repeated sediment flows. Mud drapes cover the sub-layers and indicate the existence of flow-velocity stagnant stages between each sediment flow. Current reversals within the sub-layers indicate the repeated occurrence of the up- and return-flows.

The tsunami deposits are vertically divided into four depositional units, Tna to Tnd in ascending order, reflecting the temporal change of wave sizes in the tsunami wave trains. Unit Tna is relatively fine-grained and indicative of small tsunami waves during the early stage of the tsunami. Unit Tnb is a protruding coarse-grained and thickest-stratified division and is the result of a relatively large wave group during the middle stage of the tsunami. Unit Tnc is a fine alternation of thin sand sheets and mud drapes, deposited from waning waves during the later stage of the tsunami. Unit Tnd is deposited during the final stage of the tsunami and is composed mainly of suspension fallout. Cyclic build up of these sub-layers and depositional units cannot be explained by storm waves with short wave periods of several to ten seconds common in small bays.     

Numerical modeling of a landslide-generated tsunami following a potential explosion of the Montserrat volcano

The explosion of the Montserrat volcano (Caribbean Sea) could trigger a major landslide and lead to the generation of a tsunami in the Caribbean Sea. In the worst case scenario, the volume of material reaching the sea has been estimated at 80 millions of cubic meters. The sliding of this mass and the generation of the associated tsunami have been simulated numerically, assuming that the debris behave like a heavy fluid flowing into the sea. The numerical model solves the 3D Navier-Stokes equations for a mixture composed of rocks and water. The generated water waves is then propagated around the coast of Montserrat by means of a shallow water model. The numerical results show that the water heights above sea level are higher than 5 meters within a radius of 5 km of the source.     

The 1987–88 Alaskan Bight tsunamis: Deep ocean data and model comparisons

Excellent deep ocean records have been obtained of two tsunamis recently generated in the Alaskan Bight on 30 November 1987 and 6 March 1988, providing the best available data set to date for comparison with tsunami generation/propagation models. Simulations have been performed with SWAN, a nonlinear shallow water numerical model, using source terms estimated by a seafloor deformation model based on the rectangular fault plane formalism. The tsunami waveform obtained from the model is quite sensitive to the specific source assumed. Significant differences were found between the computations and observations of the 30 November 1987 tsunami, suggesting inadequate knowledge of the source characteristics. Fair agreement was found between the data and the model for the first few waves of the 6 March 1988 tsunami. Model estimates of the seismic moment and total slip along the fault plane are also in fair agreement with those derived from the published Harvard centroid solution for the 6 March 1988 event, implying that the computed seafloor deformation does bear some similarity to the actual source.     

ISPH numerical simulation of tsunami generation by submarine landslides

The present investigation focused on the numerical simulation of the gravity currents of non-Newtonian fluids by means of the incompressible smoothed particle hydrodynamics (ISPH) approach. Firstly, to solve the rheological properties of the non-Newtonian Bingham model by ISPH method, the multi-viscodensity approach has been introduced. Then, this methodology has been used to simulate the annular viscometer and landslide deformation test cases. Through simulating these test cases, the viscoplastic behavior of the non-Newtonian viscosity and propagation of tsunami waves due to underwater landslide movement have been observed. Numerical results were in good agreement with the theoretical and experimental studies and showed that this methodology can be used to investigate precisely the generation and propagation of tsunami surface waves.     

Reconstructing hydrodynamic flow parameters of the 1700 tsunami at Cannon Beach, Oregon, USA

Coastal communities in the western United States face risks of inundation by distant tsunamis that propagate across the Pacific Ocean as well as local tsunamis produced by great (M_w?>?8) earthquakes on the Cascadia subduction zone. In 1964, the M_w 9.2 Alaska earthquake launched a Pacific-wide tsunami that flooded Cannon Beach, a small community (population 1640) in northwestern Oregon, causing over $230,000 in damages. However, since the giant 2004 Indian Ocean tsunami, the 2010 Chile tsunami and the recent 2011 Tohoku-Oki tsunami, renewed concern over potential impacts of a Cascadia tsunami on the western US has motivated closer examination of the local hazard. This study applies a simple sediment transport model to reconstruct the flow speed of the most recent Cascadia tsunami that flooded the region in 1700 using the thickness and grain size of sand layers deposited by the waves. Sedimentary properties of sand from the 1700 tsunami deposit provide model inputs. The sediment transport model calculates tsunami flow speed from the shear velocity required to suspend the quantity and grain size distribution of the observed sand layers. The model assumes a steady, spatially uniform tsunami flow and that sand settles out of suspension forming a deposit when the flow velocity decreases to zero. Using flow depths constrained by numerical tsunami simulations for Cannon Beach, the sediment transport model calculated flow speeds of 6.5?C7.6?m/s for sites within 0.6?km of the beach and higher flow speeds (~8.8?m/s) for sites 0.8?C1.2?km inland. Flow speed calculated for sites within 0.6?km of the beach compare well with maximum velocities estimated for the largest tsunami simulation. The higher flow speeds calculated for the two sites furthest landward contrast with much lower maximum velocities (<3.8?m/s) predicted by numerical simulations. Grain size distributions of sand layers from the most distal sites are inconsistent with deposition from sediment falling out of suspension. We infer that rapid deceleration in tsunami flow and convergences in sediment transport formed unusually thick deposits. Consequently, higher flow speeds calculated by the sediment model probably overestimate the actual wave speed at sites furthest inland.     

A smoothing algorithm to enhance finite-element tsunami modelling: An application to the 5 February 1783 Calabrian case,Italy

Numerical simulations are essential tools for studying tsunami generation and evolution and finite-element (FE) methods are widely used, especially because of their capability in modeling water waves in basins with complex bathymetry and irregular coastlines. This paper presents the numerical simulation of an historical Italian tsunami that affected the Tyrrhenian coasts of Calabria and Sicily on 5 February 1783 following a strong destructive earthquake that was the first of a terrible sequence of seismic shocks terrifying the Calabrian population for more than two months. The numerical model is an FE model based on the nonlinear nondispersive shallow-water approximation of the Navier-Stokes equations. Since FE discretization schemes may lead to solutions undesirably affected by noise over coarse grids, in this study numerical noise is controlled by suitably smoothing the FE solution at regular time steps t _s. The performance of our smoothing algorithm is tested for significant linear cases for which an analytical solution is available.     

Visualization of tsunami waves with Amira package

In recent years numerical investigations of tsunami wave propagation have been spurred by the magnitude 9.3 earthquake along the Andaman–Sumatra fault in December, 2004. Visualization of tsunami waves being modeled can yield a much better physical understanding about the manner of wave propagation over realistic seafloor bathymetries. In this paper we will review the basic physics of tsunami wave propagation and illustrate how these waves can be visualized with the Amira visualization package. We have employed both the linear and nonlinear versions of the shallow-water wave equation. We will give various examples illustrating how the files can be loaded by Amira, how the wave-heights of the tsunami waves can be portrayed and viewed with illumination from light sources and how movies can be used to facilitate physical understanding and give important information in the initial stages of wave generation from interaction with the ambient geological surroundings. We will show examples of tsunami waves being modeled in the South China Sea, Yellow Sea and southwest Pacific Ocean near the Solomon Islands. Visualization should be a part of any training program for teaching the public about the potential danger arising from tsunami waves. We propose that interactive visualization with a web-portal would be useful for understanding more complex tsunami wave behavior from solving the 3-D Navier–Stokes equation in the near field.     

Evaluation of tsunami impacts on shallow marine sediments: An example from the tsunami caused by the 2003 Tokachi-oki earthquake, northern Japan

A combined approach of field geology and numerical simulation was conducted for evaluating the tsunami impacts on the shelf sediments. The 2003 Tokachi-oki earthquake, M 8.0, that occurred on 25 September 2003 off southeastern Hokkaido, northern Japan, generated a locally destructive tsunami. Maximum run-up height of the tsunami waves reached 4 m above sea level. In order to estimate the tsunami impacts on shallow marine sediments, we compared pre- and post-tsunami marine sediments in water depths of 38–112 m in terms of grain size, sedimentary structure, and microfossil content. Decreases of fine fractions, especially finer than very fine sand, which led to coarsen the mean grain size, were detected in the inner shelf of the northern part of the study area. Foraminiferal assemblages also changed in the coarsened sediments. On the other hand, the other shelf sediments largely unchanged or slightly fined. We also simulated the tsunami wave velocity and direction, and grain size entrained by the modeled tsunami. The numerical simulation resulted in that the 2003 tsunami could transport very fine sand in water depths shallower than 45–95 m at the northern part of the study area. This is comparable with the actual grain-size changes after the tsunami had passed. However, some storms and tidal currents might also be possible to stir the surface sediments after the pre-tsunami survey, so we could not conclude that the grain-size changes had been caused only by the tsunami. Nevertheless, a combined approach of sampling and modeling was powerful for estimating the tsunami impacts under the sea.     

Detailing the impact of the Storegga Tsunami at Montrose,Scotland

The Storegga tsunami, dated in Norway to 8150±30 cal. years BP, hit many countries bordering the North Sea. Run-ups of >30 m occurred and 1000s of kilometres of coast were impacted. Whilst recent modelling successfully generated a tsunami wave train, the wave heights and velocities, it under-estimated wave run-ups. Work presented here used luminescence to directly date the Storegga tsunami deposits at the type site of Maryton, Aberdeenshire in Scotland. It also undertook sedimentological characterization to establish provenance, and number and relative power of the tsunami waves. Tsunami model refinement used this to better understand coastal inundation. Luminescence ages successfully date Scottish Storegga tsunami deposits to 8100±250 years. Sedimentology showed that at Montrose, three tsunami waves came from the northeast or east, over-ran pre-existing marine sands and weathered igneous bedrock on the coastal plain. Incorporation of an inundation model predicts well a tsunami impacting on the Montrose Basin in terms of replicate direction and sediment size. However, under-estimation of run-up persisted requiring further consideration of palaeotopography and palaeo-near-shore bathymetry for it to agree with sedimentary evidence. Future model evolution incorporating this will be better able to inform on the hazard risk and potential impacts for future high-magnitude submarine generated tsunami events.     

Numerical Simulation of the 1969 Portuguese Tsunami by a Finite Element Method

On 28 February 1969, the coasts of Portugal, Spain and Morocco were affected by sea waves generated by a submarine earthquake (Ms = 7.3) with its epicenter located off Portugal. The propagation of this tsunami has been simulated by a finite element numerical model solving the Boussinesq equations. These equations have been discretized using the finite element Galerkin method and a Crank–Nicholson scheme in time. The model is validated by investigating the propagation of a solitary wave over a flat bottom. The grid sizes for the 1969 event have been determined by one-dimensional tests offshore and in shallow water regions. The two-dimensional simulation of the 1969 tsunami is carried out using the hydraulic source calculated from the geophysical model of Okada and seismic parameters of Fukao. The modeled waves are compared with the recorded ones with respect to travel times, maximum amplitudes and periods of the signal. The comparison between Boussinesq and shallow-water models shows that the effects of frequency dispersion are minor. Good agreement is found for most of the studied gauges.     

Modeling the 2004 Sumatra tsunami at Seychelles Islands: site-effect analysis and comparison with observations

The M _w = 9.1 mega-thrust Sumatra–Andaman earthquake that occurred on December 26, 2004, was followed by a devastating tsunami that killed hundreds of thousands of people and caused catastrophic effects on human settlements and environments along many coasts of the Indian Ocean, where even countries very far from the source were affected. One of these cases is represented by the Republic of Seychelles, where the tsunami reached the region about 7 h after the earthquake and produced relevant damages, despite the country was more than 4,500 km far from the seismic source. In the present work, we present and discuss a study of the 2004 Sumatra tsunami by means of numerical simulations with the attention focused on the effects observed at the Seychelles Archipelago, a region never previously investigated with this approach. The case is interesting since these islands lay on a very shallow oceanic platform with steep slopes so as the ocean depth changes from thousands to few tens of meters over short distances, with significant effects on the tsunami propagation features: the waves are strongly refracted by the oceanic platform and the tsunami signal is modified by the introduction of additional frequencies. The study is used also to validate the UBO-TSUFD numerical code on a real tsunami event in the far field, and the results are compared with the available observations, i.e., the sea level time series recorded at the Pointe La Rue station, Mahé Island, and run-up measurements and inundation lines surveyed few weeks after the tsunami at Praslin Island, where the tsunami hit during low tide. Synthetic results are found in good agreement with observations, even though some of the observations remain not fully solved. Moreover, simulations have been run in high-tide condition since the 2004 Sumatra tsunami hitting at high tide can be taken as the worst-case scenario for the Seychelles islands and used for tsunami hazard and risk assessments.     

扭转导波在锚固锚杆中传播的数值模拟

采用有限元数值模拟的方法研究了扭转导波在锚固锚杆中的传播性质。建立了自由锚杆和锚固锚杆的有限元模型,在锚杆顶端激发20～60 kHz扭转导波信号,计算得到导波在自由锚杆和锚杆锚固段的传播速度值与理论值吻合很好,证明了扭转导波数值模拟方法的有效性。数值模拟结果表明：随着激发波频率的增大,扭转导波在自由锚杆和锚杆锚固段中的衰减值均呈线性递增趋势,导波在锚杆锚固段上界面的反射回波逐渐减弱;扭转导波在锚杆锚固段的衰减值较大,无法在锚杆顶端采集到锚杆底端反射回波信号,所以扭转导波不适用于锚杆长度的检测;随着锚固介质弹性模量的增大,同一频率扭转导波在锚杆锚固段上界面的反射波逐渐增强。通过检测扭转导波在锚杆锚固段上界面的反射回波,可以确定锚固介质弹性模量的大小。