NUMERICAL SIMULATION OF TSUNAMIIN INDIAN OCEAN

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EUROPEAN SCHOOL OF ADVANCED STUDIES INREDUCTION OF SEISMIC RISKROSE SCHOOLNUMERICAL SIMULATION OF TSUNAMIIN INDIAN OCEANA Dissertation Submitted inPartial Fulfillment of the Requirements for theMaster Degree in Earthquake EngineeringByJ.M. RUWAN SANJEEWA APPUHAMYSupervisors:Prof. STEFANO TINTIProf. CARLO G. LAIMay, 2007Universit degliStudi di PaviaIstitutoUniversitariodi Studi Superiori

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The dissertation entitled Numerical Simulation of Tsunami in Indian Ocean, by J.M. RuwanSanjeewa Appuhamy, has been approved in partial fulfillment of the requirements for MasterDegree in Earthquake Engineering.Prof. Stefano TintiProf. Carlo G. Lai

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Numerical Modeling of Tsunami in Indian Ocean Page iABSTRACTKeywords:Tsunami, Sri Lanka, Run-up, Inundation, Numerical Simulation, Safe area, Warning,Evacuation, Save the nation.The tsunami is the most formidable of all natural hazards. It is usually generated as a result ofseismotectonic motions of the ocean bottom in the seismic source zone. Tsunami waves propagatefar from the source and can cause damage even in regions where the earthquake was notmanifested. The unexpectedness of tsunami is an additional risk factor.The 26thof December 2004 was an unforgettable day for all Sri Lankans as well as for the wholeworld. On that fateful day, tsunami waves struck the Eastern and Southern coasts of Sri Lanka aswell as parts of Northern and Western coasts sweeping people away, causing flooding anddestruction of infrastructures. When the huge waves surged up the coasts of Sri Lanka, thedevastation of a tsunami brought forth a surge of generosity the likes of which the world hasrarely seen. The tsunami waves were caused by an earthquake, measuring 9.1 on the Richter scalethat occurred in the sea near Sumatra, Indonesia. The other neighboring countries affected by thistsunami were Indonesia, India, Maldives, Somalia and Thailand. Since many Sri Lankans did nothave any previous experience of this nature, the damage caused to their lives was unbelievable.Thousands of people were displaced and disappeared or killed within a very short time.Often the only way to determine the potential run-ups and inundation from a local or distanttsunami is to use numerical modeling, since data from past tsunamis is usually insufficient.Models can be initialized with potential worst case scenarios for the tsunami sources or for thewaves just offshore to determine corresponding worst case scenarios for run-up and inundation.Models can also be initialized with smaller sources to understand the severity of the hazard for theless extreme but more frequent events. This information is then the basis for creating tsunamievacuation maps and procedures.It then might be possible to use such simulations to predict tsunami behaviour immediately afteran earthquake is detected and the government or the responsible authorities can take the necessaryactions to evacuate the innocent residents to the safe areas shown in evacuation maps which havebeen created by numerical simulations. Since Sri Lankan island is located far enough from thedestructive tsunamigenic plate boundaries, accurate and well timing warning can make our peopleeducate enough to self evacuate to those safer locations and save the nation in future disasters.

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Numerical Modeling of Tsunami in Indian Ocean Page iiACKNOWLEDGEMENTSI would like to express my deepest gratitude to Prof. Stefano Tinti and Prof. Carlo G. Lai forguiding me in this research and being extremely supportive throughout the whole research period.It is essential to state that without their kind and remarkable supervision, this work could have notbeen completed at all.Also I would like to thank Prof. Laura Kong (Director, UNESCO-IOC) for giving me the greatopportunity and sponsoring to attend to the International Training workshop conducted byUNESCO-IOC on Numerical Modeling of Tsunami in Indian Ocean at Oostende, Belgiumwhich really helped me to conduct this dissertation research work. Also I would like to thank Prof.Emile Okal, Prof. Costas Synolakis, Prof. Ahmet Yalciner and Dr. Andrey Zaytsev for theirexcellent guidance during the training period at Belgium. Also my profound gratitude goes to thewhole above mention team for providing me the AVI-NAMI tsunami simulation program for thisresearch work.It is my pleasure to be thankful to Dr. Beatriz Brizuela and the whole Tsunami Research Team ofthe University of Bologna (Dr. Alberto Armigliato, Dr. Filippo Zamboni, Dr. Roberto Tonini, Dr.Anna Manucci, Dr. Gian Luca Pagnoni, Dr. Sara Carolina and Dr. Lidia Bressan) for theirunconditional help in numerous ways during this research period.And I would like to give my heartiest compliments to Prof. Charles L. Mader (Director, Tsunamisociety, Holonolu, Hawaii), Dr. Nimal Wijerathne (Senior Lecturer, University of Ruhuna, SriLanka), Prof. Charitha Pattiaratchi (Senior Professor, University of Western Australia), Dr. K.Arulanathan and Mr. S.U.P. Jinadasa (NARA, Sri Lanka) for their kind contribution and sendingso many required materials for this research.

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Numerical Modeling of Tsunami in Indian Ocean Page iiiNUMERICAL SIMULATION OF TSUNAMI IN INDIAN OCEANINDEXABSTRACT..iACKNOWLEDGEMENTS....iiINDEX......iiiLIST OF TABLES..viLIST OF FIGURES...viiCHAPTER 1: NATURAL HAZRDS1.1 Introduction......11.2 Floods...11.3 Droughts...21.4 Hurricanes....21.5 Volcanic Eruptions.......31.6 Earthquakes..4CHAPTER 2: TSUNAMI2.1 Introduction112.2 Tsunamis vs. Wind Waves.132.3 Tsunami Generation...152.3.1 Initiation..152.3.2 Split.162.3.3 Amplification..172.3.4 Run-up....172.4 Tsunami Wave Characteristics..182.4.1 Wave Definitions182.4.2 Basic Equations of the Wave Motion.192.4.2.1 The Velocity Potential...192.4.2.2 Wave Length and Wave Celerity...202.4.2.3 Constancy of Wave Period.202.4.3 Tsunami Wave Velocity, Wavelength and Period..212.5 Destruction due to Tsunami...232.6 Tsunami Intensity Scale.25Page No.

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Numerical Modeling of Tsunami in Indian Ocean Page ivCHAPTER 3: HYSTORICAL TSUNAMI EVENTS3.1 Introduction273.2 Pacific Ocean Earthquakes and Tsunamis.273.2.1 April 1, 1946 Aleutian Earthquake and Tsunami...273.2.2 November 4, 1952 Kamchatka Earthquake and Tsunami..283.2.3 March 9, 1957 Aleutian Earthquake and Tsunami.293.2.4 May 2, 1960 Chilean Earthquake and Tsunami..293.2.5 March 28, 1964 Alaska Earthquake and Tsunami..303.2.6 September 2, 1992 Nicaragua Earthquake and Tsunami....313.2.7 July 12, 1993 Okushiri, Japan Earthquake and Tsunami323.2.8 October 4, 1994 Russia- Kuril Islands, Shikotan Eqk. & Tsunami....323.2.9 November 15, 1994 Philippines- Mindora Earthquake & Tsunami...323.2.10 October 9, 1995 Mexico-Manzanilo Earthquake and Tsunami323.2.11 February 21, 1996 Peru- Northern Earthquake and Tsunami...333.2.12 July 17, 1998 Papua New Guinea (PNG) Earthquake & Tsunami...333.2.13 November 26, 1999 Vanuatu Earthquake and Tsunami...343.2.14 June 23, 2001 Peru-Southern Earthquake and Tsunami...343.2.15 January 2, 2002 Vanuatu Earthquake and Tsunami.343.3 Indian Ocean Earthquakes and Tsunamis..353.3.1 December 12, 1992 Indonesia Flores Island Eqk. & Tsunami353.3.2 June 2, 1994 Indonesia, Java Earthquake and Tsunami..353.3.3 May 3, 2000 Indonesia Sulawesi Island Earthquake & Tsunami....363.3.4 December 26, 2004 Indian Ocean Earthquake and Tsunami..363.4 The Great Earthquake and Mega Tsunami on 26th December 2004.373.4.1 Tectonics of the Sumatra-Andaman Islands...393.4.2 Historical Events in Sumatran Region413.4.3 Tsunami Generation from the 2004 M=9.1 Sumatra Earthquake...42CHAPTER 4: COMPARISON OF LOCAL AND INTERNATINAL DAMAGEASSESSMENTS4.1 Introduction454.2 Damage Assessments conducted by Local Authorities in Sri Lanka454.3 Damage Assessments conducted by International Organizations.554.3.1 Tsunami Heights.554.3.2 Tsunami Sand Deposits..584.3.2 Tsunami impact on Structures, Highways and Boat Harbors60CHAPTER 5: RELATIONSHIP BETWEEN RUN-UP HEIGHT AND THEHORIZONTAL INUNDATION LENGTH5.1 Introduction635.2 Continental Margin of Sri Lanka & the Bathymetry around Country...63

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Numerical Modeling of Tsunami in Indian Ocean Page v5.3 Run-up and Inundation Length..645.4 Relationship between Run-up Height and the Inundation Length.65CHAPTER 6: NUMERICAL SIMULATION OF TSUNAMI6.1 Governing Equations.726.1.1 Shallow Water Theory726.1.2 Bottom Friction...746.1.3 Governing Equation756.1.4 Note on convection terms...756.2 Numerical Scheme.766.2.1 Numerical Scheme for Linearized Equation...766.2.2 Numerical Scheme for Convection Terms..786.2.3 Numerical scheme for bottom friction term79CHAPTER 7: AVI-NAMI PROGRAM...81CHAPTER 8: TSUNAMI SIMULATION RESULTS8.1 Introduction828.2 Indian Ocean Tsunami - 26th December 2004 Event838.2.1 December 26th, 2004 Event (Mw= 9.1)..838.2.2 Comparison of Numerical Simulation Results of Dec. 26th, 2004 Event...918.2.3 December 26th, 2004 Event (Simulation with Mw= 8.8)...948.2.4 December 26th, 2004 Event (Simulation with Mw= 8.5, 8.0, 7.5, 7.0)..968.2.5 Magnitude vs. Water Level Variation....988.3 Expected Indian Ocean Tsunami Event 1.1008.4 Expected Indian Ocean Tsunami Event 2.1038.5 Expected Indian Ocean Tsunami Event 3.110CHAPTER 9: CONCLUSIONS.114CHAPTER 10: REFERENCE, GLOSSARY OF TSUNAMI MODELING & APPENDIX10.1 Reference...11610.2 Glossary of Tsunami Modeling.12110.3 APPENDIX Manual of AVI-NAMI Program....13110.3.1 Data Input and Simulation Process.13110.3.1.1 Creating the Initial wave from Different Sources....13110.3.1.2 Creating an Initial wave from an Impact.13210.3.1.3 Generating the Sea State at specific time intervals of Tsunami..13310.3.2 Calculating Distribution of Run-ups..13510.3.2.1 1-Event Option13510.3.2.2 All event Option..13610.3.3 Plotting the Output Files and Preparing Plots for Animations...13710.3.4 Camera Settings.13810.3.5 Create Animations.13910.3.6 Create Gauge Point File.140

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Numerical Modeling of Tsunami in Indian Ocean Page viLIST OF TABLESTable 1.1:Earthquakes with 1,000 or More Deaths since 1900...5Table 2.1:Wave Classification...14Table 2.2:Tsunami Intensity Scale.25Table 3.1:The 10 largest earthquakes in the world37Table 4.1:Damaged Housing Units and Tsunami Affected Population in Sri Lankaaccording to the GN Basis 46Table 4.2:Damaged Housing Units, Tsunami Affected Population and Dead & MissingPeople in Sri Lanka according to the Districts Basis.....49Table 5.1:Measured Maximum Run-up and Inundation Lengths..65Table 5.2:Values of Measured Maximum Run-up, Measured and Predicted InundationLengths..71Table 6.1:Values of Coefficient of Bottom Friction..........74Table 8.1:Corresponding Fault Data for Different Earthquake Magnitudes...101Table 8.2:Expected Wave Height and the Wave Arrival Time of 1stLeading ElevationWave.....113Table 8.3:Expected Maximum Water Level Elevation and the Peak Wave Arrival Time..113Page No.

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Numerical Modeling of Tsunami in Indian Ocean Page viiLIST OF FIGURESFigure 1.1:Flooding caused by heavy rains in Asia.1Figure 1.2:Merciless of the Drought2Figure 1.3:Two photographs taken during a Hurricane...2Figure 1.4:The different outcomes of a volcanic eruption and the Mt. Etna, Sicily3Figure 1.5:The effects of the ground shaking due to an earthquake4Figure 2.1:General view of a Tsunami wave.12Figure 2.2:Basic differences between Wind wave and a Tsunami13Figure 2.3:Initiation of a Tsunami wave16Figure 2.4:Splitting of a Tsunami wave.16Figure 2.5:Amplification of a Tsunami wave17Figure 2.6:Runup of a Tsunami wave17Figure 2.7:The basic profile of a Sinusoidal wave18Figure 2.8:The tsunami window.22Figure 2.9:Different Types of Damages which causes by Tsunami..23Figure 3.1:Destruction of the lighthouse at Scotch Cap on Unimak Island, Alaska.27Figure 3.2:November 4, 1952 Kamchatka Earthquake and Tsunami28Figure 3.3:May 2, 1960 Chilean Earthquake and Tsunami...29Figure 3.4:March 28, 1964 Alaska Earthquake and Tsunami...30Figure 3.5:July 17, 1998 Papua New Guinea (PNG) Earthquake and Tsunami33Figure 3.6:December 12, 1992 Indonesia Flores Island Earthquake and Tsunami35Figure 3.7:Tsunami damage in East Java..35Figure 3.8:The earthquake epicenter, aftershocks, and the extent of the main faultrupture for the M=9.1December 26, 2004 earthquake and the M=8.7March 28, 2005 earthquake..38Figure 3.9:Tectonic base map of the Sumatra subduction zone showing major faults.39Figure 3.10:Oceanic- oceanic convergence...40Figure 3.11:Types of faulting of an oblique subduction zone...40Figure 3.12:Tsunami triggered locations in the Indian Ocean since 176241Figure 3.13:Variation of local tsunami intensity with moment magnitude of the eqk..42Figure 3.14:Base map of the Sumatra subduction zone43Figure 3.15:Generation of Tsunami due the 26thDecember 2004 earthquake..44Page No.

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Numerical Modeling of Tsunami in Indian Ocean Page viiiFigure 4.1:Total Damage of Housing Units according to the GN Divisions Basis..48Figure 4.2:Total Affected Population according to the GN Divisions Basis...48Figure 4.3:Total Affected Population according to the Districts Basis49Figure 4.4:Total Dead and Missing People according to the Districts Basis...50Figure 4.5:Total Damage of Housing Units according to the Districts Basis..50Figure 4.6:Tsunami Affected People and Damaged Houses in Sri Lanka in all Districts.51Figure 4.7:Train Disaster at Paraliya.52Figure 4.8:Galle Bus Stand53Figure 4.9:Behind the Galle Harbour53Figure 4.10:Close to Galle Bridge.53Figure 4.11:Close to Kittangeya Hospital and Dickson Place in Galle.53Figure 4.12:Tsunami attack in Panadura...54Figure 4.13:Tsunami attack in Fishery Harbours..54Figure 4.14:Measured tsunami run-up and Maximum tsunami heights56Figure 4.15:Tsunami water mark at 150 m away from the shoreline at Mankerni56Figure 4.16:Tsunami water mark at Yala Safari Hotel..56Figure 4.17:Tsunami water mark at 220 m away from the shoreline at Kalmunai...57Figure 4.18:Tsunami overtopped the Bridge of 3.7 m above sea level at Kuchchaveli57Figure 4.19:Tsunami Water marks at Payagala.57Figure 4.20:Variation of Tsunami Sand Deposition in Mankerni.....58Figure 4.21:Measured maximum thicknesses of tsunami deposits and minimum inlandextent of tsunami sediments...59Figure 4.22:Tsunami Sand Deposits in Nilaweli Hotel.59Figure 4.23:Soil Erosions due to Tsunami....60Figure 4.24:Damaged Buildings nearly 500m of the coast in Kalmunai..60Figure 4.25:Tsunami removed the houses at about 75m inland at Mankerni...61Figure 4.26:Rooms at the Yala Safari Resort61Figure 4.27:Complete destruction of houses at Hikkaduwa..61Figure 4.28:Destruction of Electricity line and Communication tower at Hambantota61Figure 4.29:Road Destruction at Kattankudy62Figure 4.30:Railway track Destruction at Payagala..62Figure 4.31:A dredge washed ashore in Galle Port...62Figure 4.32:Tilt Public Bathroom at Thangalla.62Figure 4.33:Destruction of the Arugam Bay Bridge..62Figure 5.1:Tsunami wave propagation alone the lands.64Figure 5.2:Measured Maximum Run-up and Inundation Lengths66

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Numerical Modeling of Tsunami in Indian Ocean Page ixFigure 5.3:Geological factors k used for finding a relationship between Run-up & Inundation..67Figure 5.4:Variation of Measured Maximum Run-up and Inundation Lengths68Figure 5.5:Proposed Run-up vs. Horizontal Inundation Variation-169Figure 5.6:Proposed Run-up vs. Horizontal Inundation Variation-269Figure 5.7:Proposed Run-up vs. Horizontal Inundation Variation-370Figure 5.8:Proposed Run-up vs. Horizontal Inundation Variation-470Figure 5.9:Comparison of Run-up vs. Horizontal Inundation Lengths from differentPredicted Methods....71Figure 6.1:Central Finite Difference Representations...76Figure 6.2:The Point Schematics for the Numerical Scheme77Figure 8.1:Four major different Tsunamigenic Scenarios.82Figure 8.2:Initial Vertical Sea Floor Offset for Dec. 26th, 2004 Event (Mw=9.1)...83Figure 8.3:Maximum and Minimum Water Level Elevations for Dec. 26th,2004 Event (Mw=9.1)..84Figure 8.4:Sea States at Different Instants for Dec. 26th, 2004 Event (Mw=9.1).85Figure 8.5:Gauge point Locations around Sri Lanka used for the Simulation..87Figure 8.6:Water Level Variation in Jafna for Dec. 26th, 2004 Event (Mw=9.1)....87Figure 8.7:Water Level Variation in Trincomalee for Dec. 26th, 2004 Event (Mw=9.1)....88Figure 8.8:Water Level Variation in Kalmunei for Dec. 26th, 2004 Event (Mw=9.1).88Figure 8.9:Water Level Variation in Yala for Dec. 26th, 2004 Event (Mw=9.1).89Figure 8.10:Water Level Variation in Hambantota for Dec. 26th, 2004 Event (Mw=9.1)...89Figure 8.11:Water Level Variation in Galle for Dec. 26th, 2004 Event (Mw=9.1)..90Figure 8.12:Water Level Variation in Colombo for Dec. 26th, 2004 Event (Mw=9.1)....90Figure 8.13:Water Level Variation in Different cities around Sri Lanka forDec. 26th, 2004 Event (Mw=9.1)..91Figure 8.14:Initial Vertical Sea Floor Offset for Sumatra Event..92Figure 8.15:Sea Floor Offset after two hours for Sumatra Event.92Figure 8.16:Tsunami wave arrivals times for Sumatra Event..93Figure 8.17:Minimum & Maximum Water Level Elevations for Sumatra Event....93Figure 8.18:Water Level Variations in Different Cities for Sumatra Event.....94Figure 8.19:Initial Vertical Sea Floor Offset for Dec. 26th, 2004 Event (Mw=8.8)........95Figure 8.20:Maximum & Minimum Water Level Elevations for Dec. 26th,2004 Event (Mw=8.8)...96Figure 8.21:Initial Vertical Sea Floor Offset for Dec. 26th, 2004 Event.(Mw=8.5, 8.0, 7.5 & 7.0)..96Figure 8.22:Maximum and Minimum Water Level Elevations for Dec. 26th,2004 Event (Mw=8.5, 8.0, 7.5 & 7.0)....97

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Numerical Modeling of Tsunami in Indian Ocean Page xFigure 8.23:Water Level Elevation Variation with the Eqk. Mag. at 25m Sea depth...98Figure 8.24:Expected Water Level Elevation Variation with the Eqk. Mag. at the Shore...98Figure 8.25:Water Level Elevation Variation at YALA with the Eqk. Magnitudeat 25m Sea depth...99Figure 8.26:Expected Water Level Elevation Variation at YALA with the Eqk.Magnitude at the Shore.99Figure 8.27:Initial Vertical Sea Floor Offset for Expected Event-1...100Figure 8.28:Maximum and Minimum Water Level Elevations for Expected Event-1...100Figure 8.29:Sea States at Different Instants for Expected Event-1.101Figure 8.30:Initial Vertical Sea Floor Offset for Expected Event-2103Figure 8.31:Maximum and Minimum Water Level Elevations for Expected Event-2...103Figure 8.32:Sea States at Different Instants for Expected Event-2.104Figure 8.33:Water Level Variation in Jafna for Expected Event-2.106Figure 8.34:Water Level Variation in Trincomalee for Expected Event-2.106Figure 8.35:Water Level Variation in Kalmunei for Expected Event-2..107Figure 8.36:Water Level Variation in Yala for Expected Event-2......107Figure 8.37:Water Level Variation in Hambantota for Expected Event-2..108Figure 8.38:Water Level Variation in Galle for Expected Event-2.108Figure 8.39:Water Level Variation in Colombo for Expected Event-2...109Figure 8.40:Water Level Variation in Different cities around Sri Lanka for ExpectedEvent-2....109Figure 8.41:Initial Vertical Sea Floor Offset for Expected Event-3...110Figure 8.42:Maximum and Minimum Water Level Elevations for Expected Event-3...110Figure 8.43:Sea States at Different Instants for Expected Event-3.111Figure 10.1:Window of the Initial Wave Generation due to a Seismic Fault.....131Figure 10.2:Window of the Initial Wave Generation due to an Impact......132Figure 10.3:Parameters used for the Impact Wave generation.......133Figure 10.4:Window of the Tsunami Source Input.134Figure 10.5:Window of the Sea State calculation for specified Time Intervals.134Figure 10.6:Window of the Run-up Calculation for 1-Event Option.....136Figure 10.7:Window of the Run-up Calculation for All Event Option......136Figure 10.8:Window of the Plotting of Output Files.....137Figure 10.9:Window of the Plotting of Output Files......138Figure 10.10:Window of the Animation Creation......139Figure 10.11:Window of the Animation Creation......140

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Numerical Modeling of Tsunami in Indian Ocean Page 1CHAPTER 1: NATURAL HAZARDS1.1 IntroductionHazards can be simply defined as unpreventable natural events that, by their nature, may exposeour Nations population to the risk of death or injury and may damage or destroy private property,societal infrastructure, and agricultural or other developed land. Hazards include floods, droughts,hurricanes, volcanic eruptions, earthquakes etc.1.2 FloodsFlowing water towards the inland due to heavy rains with high intensity and/or long duration canbe simply defined as floods. Floods are the most common and widespread of all natural disasters,except fire. Floods have been an integral part of the human experience ever since the start of theagricultural revolution when people built the first permanent settlements on the great riverbanks ofAsia and Africa. Seasonal floods deliver valuable topsoil and nutrients to farmland and bring lifeto otherwise infertile regions of the world such as the Nile River Valley. Flash floods and large100-year floods, on the other hand, are responsible for more deaths than tornadoes or hurricanes.Figure 1.1:Flooding caused by heavy rains in Asia[Cambridgeshire, U.K. floods, February 2001][http://newsfromrussia.com/accidents/2005/09/27/63775.html]

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Numerical Modeling of Tsunami in Indian Ocean Page 21.3 DroughtsBasically the converse of flooding can be defined as the droughts and worldwide, since 1967,drought alone has been responsible for millions of deaths and has cost hundreds of billions ofdollars in damage. Many different climatic events can trigger crop failures including excessrainfall leading to flood damage or crop disease, heat waves, drought, fire, unexpected cold snaps,severe storms, climate-related disease outbreaks, and insect invasions. Large-scale weatherpatterns such as El Nio, La Nia, and the Pacific Decadal Oscillation affect agriculture world-wide by changing rainfall patterns.Figure 1.2:Merciless of the Drought1.4 HurricanesFew things in nature can compare to the destructive force of a hurricane. In fact, during its lifecycle a hurricane can expend as much energy as 10,000 nuclear bombs. Hurricane winds blow in alarge spiral around a relative calm centre known as the eye. The eye is generally 20 to 30miles wide, and the storm may extend outward 400 miles. As a hurricane approaches, the sky willbegin to darken and winds will grow in strength. As a hurricane nears land, it can bring torrentialrains, high winds, and storm surges. August and September are peak months during the hurricaneseason that lasts from June 1 through November 30.Figure 1.3:Two photographs taken during a Hurricane[www.archives.qld.gov.au/.../images/twentytwo.asp][www.nwri.ca/threats2full/ch3-1-e.html][Hurricane Rita II NASA][Hurricane Katrina, USA - Sandy]

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Numerical Modeling of Tsunami in Indian Ocean Page 31.5 Volcanic EruptionsWe could say a volcano is a liquid rock plumbing system which extends from several tens ofkilometers depth to the Earths surface, and includes the near vent deposits of eruptions. Volcaniceruptions are one of Earths most dramatic and violent agents of change. Not only can powerfulexplosive eruptions drastically alter land and water for tens of kilometers around a volcano, buttiny liquid droplets of sulfuric acid erupted into the stratosphere can change our planet's climatetemporarily. Eruptions often force people living near volcanoes to abandon their land and homes,sometimes forever. Those living farther away are likely to avoid complete destruction, but theircities and towns, crops, industrial plants, transportation systems, and electrical grids can still bedamaged by tephra, lahars, and flooding.Figure 1.4:The different outcomes of a volcanic eruption and a picture of the Mt. Etna, SicilyScientists have estimated that by the year 2000, the population at risk from volcanoes is likely toincrease to at least 500 millions, which is comparable to the entire worlds population at thebeginning of the seventeenth century. Clearly, scientists face a formidable challenge in providingreliable and timely warnings of eruptions to so many people at risk.[Image credit: Tom Pfeiffer][Picture credit: USGS]

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Numerical Modeling of Tsunami in Indian Ocean Page 41.6 EarthquakesAn earthquake is a phenomenon that results from the sudden release of stored energy in theEarths crust that creates seismic waves. At the Earths surface, earthquakes may manifestthemselves by a shaking or displacement of the ground and sometimes cause tsunamis, which maylead to loss of life and destruction of property.One of the most frightening and destructive phenomena of nature is a severe earthquake and itsterrible after-effects. As relative movement of the plates occurs, elastic strain energy is stored inthe material near the boundary as increased shear stress. When the shear stress reaches theultimate shear strength of the rock along the fault, the rock fails and the accumulated strain energyis released. Earthquakes may occur naturally or as a result of human activities. In its most genericsense, the word earthquake is used to describe any seismic event, whether a natural phenomenonor an event caused by humans, that generates seismic waves.If the earthquake occurs in a populated area, it may cause many deaths and injuries and extensiveproperty damage. Although we still cannot predict when an earthquake will happen, we havelearned much about earthquakes as well as the Earth itself from studying them. We have learnedhow to pinpoint the locations of earthquakes, how to accurately measure their sizes, and how tobuild flexible structures that can withstand the strong shaking produced by earthquakes andprotect our loved ones.Figure 1.5:The effects of the ground shaking due to an earthquake[Kobe, 1995, Japan (left) and Loma Prieta, 1989, California (right)]Earthquakes happen every day around the world, but most of them go unnoticed and cause nodamage. Large earthquakes, however, can cause serious destruction. The table here belowrepresents earthquakes that happened since 1900 and caused 1,000 or more deaths.[Picture credit: USGS][Picture credit: Tokyo University]

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Numerical Modeling of Tsunami in Indian Ocean Page 5Table 1.1:Earthquakes with 1,000 or More Deaths since 1900 (Data from: USGS)Date UTCLocationDeaths MagnitudeComments1902 04 19Guatemala14 N 91 W2,0007.51902 12 16Eastern Uzbekistan(Turkistan)40.8 N 72.6 E4,5006.41903 04 19Turkey39.1 N 42.4 E1,7001903 04 28Turkey39.1 N 42.5 E2,2006.31905 04 04India, Kangra33.0 N 76.0 E19,0007.51905 09 08Italy, Calabria39.4 N 16.4 E2,5007.91906 01 31off the coast of Ecuador1 N 81.5 W1,0008.81906 03 16Formosa, Kagi (Taiwan)23.6 N 120.5 E1,3007.11906 04 18San Francisco, California37.75 N 122.55 Wabout3,0007.8Deaths from earthquakeand fire.1906 08 17Chile, Valparaiso33 S 72 W20,0008.21907 01 14Jamaica, Kingston18.2 N 76.7 W1,6006.51907 10 21Central Asia38 N 69 E12,00081908 12 28Italy, Messina38 N 15.5 E70,000 to100,0007.2Deaths from earthquakeand tsunami.1909 01 23Iran33.4 N 49.1 E5,5007.31912 08 09Marmara Sea, Turkey40.5 N 27 E1,9507.81915 01 13Italy, Avezzano42 N 13.5 E29,98071917 01 21Indonesia, Bali8.0 S 115.4 E15,0001917 07 30China28.0 N 104.0 E1,8006.51918 02 13China,Kwangtung(Guangdong)23.5 N 117.0 E10,0007.31920 12 16China, Gansu35.8 N 105.7 E200,0007.8Major fractures, landslides.1923 03 24China31.3 N 100.8 E5,0007.31923 05 25Iran35.3 N 59.2 E2,2005.7

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Numerical Modeling of Tsunami in Indian Ocean Page 61923 09 01Japan, Kanto(Kwanto)35.0 N 139.5 E143,0007.9Great Tokyo fire.1925 03 16China, Yunnan25.5 N 100.3 E5,0007.1Talifu almost completelydestroyed.1927 03 07Japan, Tango35.8 N 134.8 E3,0207.61927 05 22China, Tsinghai36.8 N 102.8 E200,0007.9Large fractures.1929 05 01Iran38 N 58 E3,3007.41930 05 06Iran38.0 N 44.5 E2,5007.21930 07 23Italy41.1 N 15.4 E1,4306.51931 03 31Nicaragua13.2 N 85.7 W2,4005.61932 12 25China, Gansu39.7 N 97.0 E70,0007.61933 03 02Japan, Sanriku39.0 N 143.0 E2,9908.41933 08 25China32.0 N 103.7 E10,0007.41934 01 15India, Bihar-Nepal26.6 N 86.8 E10,7008.11935 04 20Formosa24.0 N 121.0 E3,2807.11935 05 30Pakistan, Quetta29.6 N 66.5 E30,000 to60,0007.5Quetta almost completelydestroyed.1935 07 16Taiwan24.4 N 120.7 E2,7006.51939 01 25Chile, Chillan36.2 S 72.2 W28,0007.81939 12 26Turkey, Erzincan39.6 N 38 E32,7007.81940 11 10Romania45.8 N 26.8 E1,0007.31942 11 26Turkey40.5 N 34.0 E4,0007.61942 12 20Turkey, Erbaa40.9 N 36.5 E3,0007.3Some reports of 1,000killed.1943 09 10Japan, Tottori35.6 N 134.2 E1,1907.41943 11 26Turkey41.0 N 33.7 E40007.61944 01 15Argentina, San Juan31.6 S 68.5 W5,0007.8Reports of as many as8,000 killed.1944 02 01Turkey41.5 N 32.5 E2,8007.4Reports of as many as5,000 killed.1944 12 07Japan, Nankaido33.7 N 136.2 E1,2238.1

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Numerical Modeling of Tsunami in Indian Ocean Page 71945 01 12Japan Mikawa34.8 N 137.0 E1,9007.11945 11 27Off the coast of Pakistan24.5 N 63.0 E4,0008Strong tsunami waves.Considerable propertydamage.1946 05 31Turkey39.5 N 41.5 E1,30061946 11 10Peru, Ancash8.5 S 77.5 W1,4007.3Landslides, greatdestruction.1946 12 20Japan, Tonankai32.5 N 134.5 E1,3308.11948 06 28Japan, Fukui36.1 N 136.2 E5,3907.31948 10 05USSR(Turkmenistan,Ashgabat)38.0 N 58.3 E110,0007.31949 07 10Khait, Tajikistan(Tadzhikistan, USSR)39.2 N 70.8 E12,0007.5Nearly all buildingsdestroyed by theearthquake and landslidesin a zone 60-65 km longand 6-8 km wide. A hugeslide, about 20 km longand 1 km wide buried thetown of Khait to a depth ofabout 30 m, moving over itat a velocity of about 100m/sec. This and otherslides in the Yasman RiverValley also buried 20villages. The death toll isestimated.1949 08 05Ecuador, Ambato1.2 S 78.5 E6,0006.8Large landslides,topographical changes.1950 08 15India, Assam, Tibet28.7 N 96.6 E1,5268.6Great topographicalchanges, landslides, floods.1953 03 18Western Turkey40.0 N 27.5 E1,1037.3Yenice destroyed andmajor damage at Gonenand Can. Felt throughoutthe Aegean Islands andsouthern Greece. Macroseismic area estimated at200 square miles. Damageestimated at $3,570,000.1954 09 09Algeria, Orleans Ville36 N 1.6 E1,2506.81957 06 27USSR(Russia)56.3 N 116.5 E1,2001957 07 02Iran36.2 N 52.7 E1,2007.41957 12 13Iran34.4 N 47.6 E1,1307.31960 02 29Morocco, Agadir30 N 9 W10,000 to15,0005.7Occurred at shallow depthjust under city.

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Numerical Modeling of Tsunami in Indian Ocean Page 81960 05 22Chile39.5 S 74.5 W5,7009.5Tsunami, volcanic activity,floods.1962 09 01Iran, Qazvin35.6 N 49.9 E12,2307.31963 07 26Yugoslavia, Skopje42.1 N 21.4 E1,1006Occurred at shallow depthjust under city.1966 08 19Turkey, Varto39.2 N 41.7 E2,5207.11968 08 31Iran34.0 N 59.0 E12,000 to20,0007.31969 07 25Eastern China21.6 N 111.9 E3,0005.91970 01 04Yunnan Province, China24.1 N 102.5 E10,0007.51970 03 28Turkey, Gediz39.2 N 29.5 E1,1006.91970 05 31Peru9.2 S 78.8 W66,0007.9$530,000,000 damage,great rock slide, floods.1971 05 22Turkey38.83 N 40.52 E1,0006.91972 04 10Iran, southern28.4 N 52.8 E5,0547.11972 12 23Nicaragua, Managua12.4 N 86.1 W5,0006.21974 05 10China28.2 N 104.0 E20,0006.81974 12 28Pakistan35.0 N 72.8 E5,3006.21975 02 04China40.6 N 122.5 E10,00071975 09 06Turkey38.5 N 40.7 E2,3006.71976 02 04Guatemala15.3 N 89.1 W23,0007.51976 05 06Italy, north-eastern46.4 N 13.3 E1,0006.51976 06 25Papua, Indonesia4.6 S 140.1 E4227.15,000 to 9,000 missing andpresumed dead.1976 07 27China, Tangshan39.6 N 118.0 E255,000(official)7.5Estimated death toll ashigh as 655,000.1976 08 16Philippines, Mindanao6.3 N 124.0 E8,0007.91976 11 24Turkey-Iran border region39.1 N 44.0 E5,0007.3Deaths estimated.1977 03 04Romania45.8 N 26.8 E1,5007.21978 09 16Iran33.2 N 57.4 E15,0007.8

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Numerical Modeling of Tsunami in Indian Ocean Page 91980 10 10Algeria, El Asnam(formerly Orleansville)36.1 N 1.4 E3,5007.71980 11 23Italy, southern40.9 N 15.3 E3,0006.51981 06 11Iran, southern29.9 N 57.7 E3,0006.91981 07 28Iran, southern30.0 N 57.8 E1,5007.31982 12 13Western Arabian Peninsula Yemen14.7 N 44.4 E2,80061983 10 30Turkey40.3 N 42.2 E1,3426.91985 09 19Mexico, Michoacan18.2 N 102.5 W9,500(official)8Estimated death toll ashigh as 30,000.1986 10 10El Salvador13.8 N 89.2 W1,0005.51987 03 06Colombia-Ecuador0.2 N 77.8 W1,00071988 08 20Nepal-India border region26.8 N 86.6 E1,4506.81988 12 07Armenia, Spitak41.0 N 44.2 E25,0006.81990 06 20Western Iran37.0 N 49.4 E40,000 to50,0007.7Landslides.1990 07 16Luzon, Philippine Islands15.7 N 121.2 E1,6217.8Landslides, subsidence,and sandblows.1991 10 19Northern India30.8 N 78.8 E2,00071992 12 12Flores Region, Indonesia8.5 S 121.9 E2,5007.5Tsunami ran inland 300meters, wave height 25m.1993 09 29India, Latur-Killari18.1 N 76.5 E9,7486.21995 01 16Japan, Kobe34.6 N 135 E5,5026.9Landslide, liquefaction.1995 05 27Sakhalin Island52.6 N 142.8 E1,9897.51997 05 10Northern Iran33.9 N 59.7 E1,5607.34460 injured; 60,000homeless.1998 02 04Hindu Kush region,Afghanistan37.1 N 70.1 E2,3235.9818 injured, 8094 housesdestroyed, 6725 livestockkilled.1998 05 30Afghanistan-TajikistanBorder Region37.1 N 70.1 E4,0006.6At least 4000 people killed,many thousands injuredand homeless inBadakhshan and TakharProvinces, Afghanistan.

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Numerical Modeling of Tsunami in Indian Ocean Page 101998 07 17Papua New Guinea2.96 S 141.9 E2,1837Thousands injured, about9500 homeless and about500 missing as a result of atsunami with maximumwave heights estimated at10 meters.1999 01 25Colombia4.46 N 75.82 W1,1856.1Over 700 missing andpresumed killed, over 4750injured and about 250,000homeless.1999 08 17Turkey40.7 N 30.0 E17,1187.6At least 50,000 injured,thousands homeless.Damage estimate at 3 to6.5 billion USD.1999 09 20Taiwan23.7 N 121.0 E2,4007.6Over 8700 injured, over600,000 homeless. Damageestimate at 14 billion USD.2001 01 26Gujarat, India23.3 N 70.3 E20,0857.6166,836 injured, 600,000homeless.2002 03 25Hindu Kush Region,Afghanistan35.9 N 69.2 E1,0006.14000 injured, 1500 housesdestroyed in the Nahrinarea. Approximately20,000 people homeless.2003 05 21Northern Algeria36.90 N 3.71 E2,2666.810,261 injured, 150,000homeless, more than 1243buildings damaged ordestroyed.2003 12 26South-eastern Iran28.99 N 58.31 E26,2006.630,000 injured, 85 percentof buildings damaged ordestroyed andinfrastructure damaged inthe Bam area2004 12 26Sumatra3.30 N 95.87 E283,1069.1Deaths from earthquakeand tsunami. The mostdevastated event in therecent past. Most of thevictims were fromIndonesia and Sri Lanka.2005 03 28Northern Sumatra,Indonesia2.07 N 97.01 E1,3138.62005 10 08Pakistan34.53 N 73.58 E80,3617.62006 05 26Indonesia7.961 S 110.446 E5,7496.3At least 5749 people werekilled, 38,568 were injuredand as many as 600,000people were displaced inthe Bantul-Yogyakartaarea. More than 127,000houses were destroyed andan additional 451,000 weredamaged in the area, withthe total loss estimated atapproximately 3.1 billionU.S. dollars.

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Numerical Modeling of Tsunami in Indian Ocean Page 11CHAPTER 2: TSUNAMI2.1 IntroductionTsunami is a Japanese term derived from the characters "tsu" meaning harbor and"nami" meaning wave. Now generally by the international scientific community it isused to describe a series of traveling waves in water produced by the displacement ofthe sea floor associated with submarine earthquakes, volcanic eruptions, orlandslides. A good definition of tsunami may be the following one: the tsunami is aseries of ocean waves of extremely long wave length and long period generated in abody of water by an impulsive disturbance that displaces the water.Tsunamis are known with different names in different nations of the world and some of them arelisted as below: Tsu Nami (Harbour wave) [Japanese] Maremoto [Italian, Spanish] Raz-de-mare [French] Flutwellen [German] Taitoko [Marquesan] vl (Waralla) [Sinhalese] (Proposed)Tsunamis can be generated when the sea floor abruptly deforms and vertically displaces theoverlying water. Earthquakes are often associated with the Earths crustal deformation; whenearthquakes occur beneath the sea, the water above the deformed area is displaced from itsequilibrium position. Waves are formed as the displaced water mass, which acts under theinfluence of gravity, attempts to regain its equilibrium. When large areas of the sea floor elevateor subside, a tsunami can be created.Large vertical movements of the Earths crust can occur at plate boundaries. Plates interact alongthese boundaries called faults. Around the margins of the Pacific Ocean, for example, denser

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Numerical Modeling of Tsunami in Indian Ocean Page 12oceanic plates slip under continental plates in a process known as subduction. Subductionearthquakes are particularly effective in generating tsunamis.Compared with wind-driven waves, tsunamis have periods, wavelengths, and velocities tens or ahundred times larger. So they have different propagation characteristics and shorelineconsequences.As a result of their long wavelengths, tsunamis behave as shallow-water waves. Shallow-waterwaves are different from wind-generated waves, the waves many of us have observed on a beach.Wind-generated waves usually have period of 0.5 to 20 seconds and a wavelength up to about 200meters. A tsunami can have a period in the range of ten minutes to two hours and a wavelength inexcess of 500 km [Prager, 1999].Figure 2.1:General view of a tsunami wave[Figure credit: Prof. Charita Pattriarachchi]It is because of their long wavelengths that tsunamis behave as shallow water waves. A wave ischaracterized as a shallow water wave when the ratio between the water depth and its wavelengthgets very small. The rate at which a wave loses its energy is inversely related to its wavelength.Since a tsunami has a very large wavelength, it will lose little energy as it propagates. Hence invery deep water, a tsunami will travel at high speeds and travel great transoceanic distances withlimited energy loss. For example, when the ocean is 6100 m deep, unnoticed tsunami travel about890 km/hr, the speed of a jet airplane. And they can move from one side of the Pacific Ocean tothe other side in less than one day.

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Numerical Modeling of Tsunami in Indian Ocean Page 132.2 Tsunamis vs. Wind WavesTsunamis are created by sudden movements or disturbances of the seafloor, submarine explosions,or impacts of large objects, such as landslides from the coastline or asteroids, or landslides thatoccur in or flow into the sea, also known as subaqueous slumps. These events trigger a series offast-moving, long waves of initial low amplitude that radiate outward in a manner resembling thewaves radiating when a pebble is dropped in the ocean. In contrast, most of the waves observed onbeaches are generated by wind dragging or disturbing the surface of the sea. Tsunamis aregenerated by disturbing the seafloor, wind waves by disturbing the ocean surface. Anothermechanism for triggering tsunamis is shaking of a closed basin, such as a reservoir, lake, orharbor. These tsunamis are also referred to as sloshing waves or seiches and sometimes they canbe observed several hours after large earthquakes even at large distances. The 1755 Great Lisbonearthquake triggered sloshing at Loch Lomond in Scotland that persisted for several hours andcaused the shoreline to advance repeatedly to elevations up to 1 m from the still water line.Figure 2.2:Basic differences between wind waves and a tsunami[Figure credit: Dept. of Earth and Space Sciences, University of Washington]In general, waves are considered deep-water waves if their wavelengthLis relatively smallcompared to the water depthdthrough which they travel. Wind waves do not feel the seaflooruntil within tens of meters from the coastline, depending on the slope of the beach. In the openocean, where depths average about 4 km, most wind waves are deep-water waves, i.e., with ashort wavelength relative to depth,d/L> 0.5. In contrast, shallow-water waves are those with along wavelength relative to depth,d/L< 1/20. The depth and nature of the seafloor stronglyinfluence how shallow-water waves propagate or travel. Because tsunamis have such longwavelengths, even when traveling through very deep water, they are considered shallow-waterwaves [Prager, 1999].

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Numerical Modeling of Tsunami in Indian Ocean Page 14Table 2.1 summarizes wave classification criteria according to relative depth and the waveparameterkdbelow.Table 2.1:Wave Classification (Ippen, 1966)Range ofd/LRange ofkd=2 d/LTypes of waves0 to 1/200 to /10Long waves (shallow-water wave)1/20 to 1/2/10 to Intermediate waves1/2 to toShort waves (deepwater waves)where:Wave number (k):2 times the number of waves per unit horizontal distance. It is equal toreciprocal of wavelength times 2 (k=2 /L).Wavelength (L) :the horizontal distance between two successive crest and troughs.Water depth (d) :the total depth of the waterThe speed or wave velocity or celeritycis calculated by dividing the wavelengthLby its periodT. The speed of deep-water waves does not depend on the depth, and the waves are dispersive, aseach component frequency of a complex spectrum propagates at its own frequency-dependentspeed. It is for this reason that complex sea states generated by storms far offshore manifestthemselves in groups of waves of approximately similar period when they strike the coast.Shallow-water waves travel at a speedc= gd, wheredis the local depth, hence all frequencies inthe spectrum of a tsunami travel at the same velocity. It is for this reason that tsunamis do not altertheir shape substantially as they propagate over fairly constant depth. Note that the classificationgiven in the table can be made less rigid as regards shallow-water waves and that many considerthe threshold ratio 1/6 or even 1/3 rather than 1/20.As they move toward the coast, tsunamis pass through varying depths and over complex seafloortopography. Changes in the depth and seafloor cause them to continuously evolve and changeshape. A tsunami generated from an earthquake off Peru may look entirely different along thePeruvian coastline as compared to when it enters a bay in California and still different when itstrikes a beach in Hawaii. Both tsunamis and wind waves behave similarly as they approach acoastline; they refract and shoal. Shoaling is the process in which the wave front steepens and thewave height increases. The front of the wave enters shallower water and moves more slowly thanthe tail of the wave, since the depth is smaller, hence the steepness at the front increases. If thewave is sufficiently steep and the continental shelf long, it eventually breaks, as the wave inessence trips over itself. However, when refracting, the crest lengths of tsunamis often causeunexpected wave patterns in refraction compared to wind waves.

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Numerical Modeling of Tsunami in Indian Ocean Page 152.3 Tsunami GenerationThe basic requirement of generation of a tsunami is the vertical movement of water mass wherehorizontal movement of the Earths crust due to an earthquake does not leads to a tsunami.Tsunamis are generated due to the gravitational oscillation of the mass of water in the ocean,following a disturbance of the ocean floor or the surface. This disturbance can be due to asubmarine earthquake, volcanic explosions at sea or a massive land slide under or close to oceans.One other class of tsunamis is that generated by impacts of comets and asteroids. When anasteroid hits the ocean at 70,000 km/h there is a gigantic explosion. The asteroid and watervaporize and leave a huge crater, typically 20 times the diameter of the asteroid (that is, a 100masteroid will create a 2 kilometer diameter crater). The water rushes back in, overshoots to create amountain of water at the middle and this spreads out as a massive wave, a tsunami. The centre ofthe crater oscillates up and down several times and a series of waves radiate out. An idea of themechanism can be obtained by bursting a balloon in a bathtub.Tsunami generation includes four major processes and they are:1. Initiation2. Split3. Amplification4. Run-up2.3.1 InitiationEarthquakes are commonly associated with ground shaking that is a result of elastic wavestraveling through the solid earth. Earthquakes generate tsunamis when the sea floor abruptlydeforms and displaces the overlying water from its equilibrium position.Submarine landslides, which often occur during a large earthquake, can also create a tsunami.During a submarine landslide, the equilibrium sea-level is altered by sediment moving along thesea-floor. Gravitational forces then propagate the tsunami given the initial perturbation of the sea-level. However, near the source of submarine earthquakes, the seafloor is permanently upliftedand down-dropped, pushing the entire water column up and down.A violent marine volcanic eruption also can create an impulsive force that displaces the watercolumn and generates a tsunami. Above water (subaerial) landslides and space born objects candisturb the water from above the surface.

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Numerical Modeling of Tsunami in Indian Ocean Page 16Once the event which initiates the tsunami occurs the potential energy that results from pushingwater above the mean sea level is then transferred to horizontal propagation of the tsunami wave(kinetic energy).For the case shown bellow, the earthquake rupture occurred at the base of the continental slope inrelatively deep water. Situations can also arise where the earthquake rupture occurs beneath thecontinental shelf in much shallower water.Figure 2.3:Initiation of a tsunami wave(Note: In the figure the waves are greatly exaggerated compared to water depth! In the openocean, the waves are at most, a few meters high and spread over many tens to hundreds ofkilometers in length.)2.3.2 SplitWithin several minutes of the initiation, the initial tsunami is split into a tsunami that travels out tothe deep ocean (distant tsunami) and another tsunami that travels towards the nearby coast (localtsunami).The height above mean sea level of the two oppositely traveling tsunamis isapproximately half that of the original tsunami. The speed at which both tsunamis travel varies asthe square root of the water depth. Therefore the deep-ocean tsunami travels faster than the localtsunami near shore.Figure 2.4:Splitting of a tsunami wave[Figure credit: USGS][Figure credit: USGS]

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Numerical Modeling of Tsunami in Indian Ocean Page 172.3.3 Amplification:Several things happen as the local tsunami travels over the continental slope. Most obvious is thatthe amplitude increases. In addition, the wavelength decreases. This results in steepening of theleading wave, an important control of wave run-up at the coast. Also the deep ocean tsunamitravels much further than the local tsunami because of the higher propagation speed. As the deepocean tsunami approaches a distant shore, amplification and shortening of the wave will occur.Figure 2.5:Amplification of a tsunami wave2.3.4 Run-upAs the tsunami wave travels from the deep water, continental slope region to the near-shoreregion, tsunami run-up occurs. Run-up is a measurement of the height of the water onshoreobserved above a reference sea level. Contrary to many artistic images of tsunamis, most tsunamisdo not result in giant breaking waves (like normal surf waves at the beach that curl over as theyapproach shore). Rather, they come in much like very strong and very fast tides (i.e., a rapid, localrise in sea level). Much of the damage inflicted by tsunamis is caused by strong currents andfloating debris. The small number of tsunamis that do break often form vertical walls of turbulentwater called bores. Tsunamis will often travel much farther inland than normal waves.Figure 2.6:Run-up of a tsunami waveNormal Sea Level[Figure credit: USGS][Figure credit: USGS]

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Numerical Modeling of Tsunami in Indian Ocean Page 182.4 Tsunami Wave CharacteristicsTsunami waves behave like shallow water waves because of its long wavelength in the deepocean. But its behavior is entirely different when it reaches the coastal area as it flows like astraight water column, rather than curl over like normal wind generated waves.2.4.1 Wave DefinitionsFigure 2.7:The basic profile of a sinusoidal waveDefinitions for the wave parameters that are partially shown in Fig. 2.7 are as follows:Wave profile ():vertical displacement of the sea surface from the still water level (SWL)as a function of time and space.Wave crest:the highest point of wave profile.Wave trough:the lowest point of wave profile.Wave amplitude (a):the vertical distance from the still water level to the wave crest.Wave height (H):the vertical distance from wave trough to wave crest. It is equal to twicethe wave amplitude. (H=2a)Wave length (L):the horizontal distance between two successive crest and troughs.Wave period (T):the time interval between the passages of two successive crests past afixed point.Wave frequency (f):the number of waves to pass a given point per unit time. It is equal toreciprocal of wave period (f=1/T).Wave number (k):2 times the number of waves per unit horizontal distance. It is equal toreciprocal of wavelength times 2 (k=2 /L).Angular wave frequency ():it is equal to wave frequency times 2 ( =2 f=2 /T).Wave HeightCrestTrough

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Numerical Modeling of Tsunami in Indian Ocean Page 19Wave celerity (C):the speed at which a waveform moves. Since the wave moves onewavelength during a wave period, the wave celerity is equal to theratio of wavelength to wave period (C=L/T). and :are the horizontal and vertical water particle displacements respectively, which arefunctions of time and depth.2.4.2 Basic Equations of the Wave Motion2.4.2.1 The Velocity PotentialThe simplest and general most useful theory is the small amplitude wave theory first presented byAiry (1845).Solving the Laplace equation develops the small amplitude wave theory for two-dimensionalperiodic waves, wherexandyare the horizontal and vertical co-ordinates respectively:02222=+yx(2.4.2.1a)With the bottom and surface conditions, the following velocity potential is obtained in an ocean ofconstant depth d,)cos(cosh)(coshtkxkddykka+=(2.4.2.1b)For a progressive wave traveling in positive x direction. The corresponding wave profile is:)sin(tkxa=Similarly the velocity potential corresponding to the wave profile:)cos(tkxa=is given by,)sin(cosh)(coshtkxkddykka+=(2.4.2.1c)

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Numerical Modeling of Tsunami in Indian Ocean Page 202.4.2.2 Wavelength and Wave CelerityThe relation between wavelength, wave period and water depth is written as)/2tanh(22LdgTL=(2.4.2.2.1)Eqn. (2.4.2.2.1) is an implicit equation, since the unknown variableLappears both in the left andright hand sides of the equation. For givenTanddvalues, to obtainLit may require to carry outseveral trial calculations. However, for convince, solutions are all ready given in graphical form,or in tables.Wave celerity is equal to the ratio of wavelength to wave period as:C=L/T(2.4.2.2.2)Thus using Eqns. (2.3.2.2.1) and (2.3.2.2.2) we get,)/2tanh(2LdgTC=(2.4.2.2.3a)2/1)/2tanh(2=LdgLC(2.4.2.2.3b)2.4.2.3 Constancy of Wave PeriodFor a simple harmonic wave train, the wave period is independent of depth. This can be proven bythe following argument. Let us suppose that the wave period can depend on the depth. Let us thentake a region where wave enters from one side and exit from the opposite side. Let us furthersuppose that at these two sides the ocean depth is different, and therefore the wave entering waveshave period T1and the outgoing waves have period T2. In a given time interval t, the number ofwaves which enter into the region is n1while, while the number of waves leaving the region is n2with n1= t / T1and n2= t / T2.Then, the number of waves which accumulate within the region is n1- n2= t (1/T1-1/T2).When the time interval t , the number of waves accumulated within the region will be depending on T1 T2. This is physically unrealistic. Then the only realistic possibility is T1= T2= T, this result holds for any depth d.

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Numerical Modeling of Tsunami in Indian Ocean Page 212.4.3 Tsunami Wave Velocity, Wavelength and PeriodClassical theory assumes a rigid seafloor overlain by an incompressible, homogeneous, and non-viscous ocean subjected to a constant gravitational field. Linear wave theory presumes that theratio of wave amplitude to wavelength is much less than one. By and large, linearity is violatedonly during the final stage of wave breaking and perhaps, under extreme nucleation conditions.In classical theory, the phase velocity c(), and group velocity u() of surface gravity waves on aflat ocean of uniform depthdare:[]dkdkgdc)(tanh)()(=(2.4.3a)and[][]+=dkdkcu)(sinh)(21)()((2.4.3b)Here k() is the wave number associated with a sea wave of frequency . Wave number connectsto wavelength () as ()=2/k(). Wave number also satisfies the relation:[]dkgk)(tanh)(2=(2.4.3c)c(),u(), and () vary widely, both as a function of ocean depth and wave period. Waveswhose velocity or wavelength varies with frequency are calleddispersive. During the propagation,dispersion pulls apart originally pulse-like waves into their component frequencies.Tsunamis may be considered waves with wavelengths greater than at least three times the oceandepth at the point of their origination. This fact fixes a short wavelength bound on tsunamis near10 km. The dimension of the sea floor disturbance fixes the upper wavelength bound. The greatestearthquakes might deform a region 500 km across. The left gray band of Fig. 2.8 colors thetsunami window (=10 to 500 km) that spans 100 to 2000 s period. Waves in the tsunamiwindow travel rapidly, reaching speeds of 160 to 250 m/s (600-900km/hr) in the open ocean.Waves at the beach travel at 10 m/s (40 km/hr) about the speed of a moped. The long period,great wavelength, and high velocity of tsunamis help account for their destructive power.

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Numerical Modeling of Tsunami in Indian Ocean Page 22in oceans of depth d sometimes include two simplifications:Discussions of waves of length 1. Long wave approximation (>>d, 1/k>>d) and2. Short wave approximation (