ArticlePDF Available

Numerical Modeling for the Krakatoa Hydrovolcanic Explosion and Tsunami

January 2006
Science of Tsunami Hazards 24(3):174

January 2006
24(3):174

License
CC BY 4.0

Authors:

Mader Consulting Co.

Krakatoa exploded August 27, 1883 obliterating 5 square miles of land and leaving a crater 3.5 miles across and 200-300 meters deep. Thirty three feet high tsunami waves hit Anjer and Merak demolishing the towns and killing over 10,000 people. In Merak the wave rose to 135 feet above sea level and moved 100 ton coral blocks up on the shore.Tsunami waves swept over 300 coastal towns and villages killing 40,000 people. The sea withdrew at Bombay, India and killed one person in Sri Lanka.The tsunami was produced by a hydrovolcanic explosion and the associated shock wave and pyroclastic flows.A hydrovolcanic explosion is generated by the interaction of hot magma with ground water. It is called Surtseyan after the 1963 explosive eruption off Iceland. The water flashes to steam and expands explosively. Liquid water becoming water gas at constant volume generates a pressure of 30,000 atmospheres.The Krakatoa hydrovolcanic explosion was modeled using the full Navier-Stokes AMREulerian compressible hydrodynamic code called SAGE which includes the high pressure physics of explosions.The water in the hydrovolcanic explosion was described as liquid water heated by the magma to 1100 degree Kelvin or 19 kcal/mole. The high temperature water is an explosive with the hot liquid water going to a water gas. The BKW steady state detonation state has a peak pressure of 89 kilobars, a propagation velocity of 5900 meters/second and the water is compressed to 1.33 grams/cc.The observed Krakatoa tsunami had a period of less than 5 minutes and wavelength of less than 7 kilometers and thus rapidly decayed. The far field tsunami wave was negligible. The air shock generated by the hydrovolcanic explosion propagated around the world and coupled to the ocean resulting in the explosion being recorded on tide gauges around the world.

Maps of Krakatoa today and before 1883.

…

The spherical model for the Krakatoa hydrovolcanic explosion.

…

The propagating hydrovolcanic explosion.

…

The density profile at later times for the hydrovolcanic explosion of Krakatoa.

…

Figures - uploaded by Charles Mader

Content may be subject to copyright.

Content uploaded by Charles Mader

Content may be subject to copyright.

Available via license: CC BY 4.0

Content may be subject to copyright.

NUMERICAL MODEL FOR THE KRAKATOA HYDROVOLCANIC

EXPLOSION AND TSUNAMI

Charles L. Mader

Mader Consulting Co.

Honolulu, HI 96825 U.S.A.

Michael L. Gittings

Science Applications International Corporation

Los Alamos, NM 87544 U.S.A.

ABSTRACT

Krakatoa exploded August 27, 1883 obliterating 5 square miles of land and leaving a

crater 3.5 miles across and 200-300 meters deep. Thirty three feet high tsunami waves

hit Anjer and Merak demolishing the towns and killing over 10,000 people. In Merak the

wave rose to 135 feet above sea level and moved 100 ton coral blocks up on the shore.

Tsunami waves swept over 300 coastal towns and villages killing 40,000 people. The

sea withdrew at Bombay, India and killed one person in Sri Lanka.

The tsunami was produced by a hydrovolcanic explosion and the associated shock

wave and pyroclastic flows.

A hydrovolcanic explosion is generated by the interaction of hot magma with ground

water. It is called Surtseyan after the 1963 explosive eruption off Iceland. The water

flashes to steam and expands explosively. Liquid water becoming water gas at constant

volume generates a pressure of 30,000 atmospheres.

The Krakatoa hydrovolcanic explosion was modeled using the full Navier-Stokes

AMR Eulerian compressible hydrodynamic code called SAGE which includes the high

pressure physics of explosions.

The water in the hydrovolcanic explosion was described as liquid water heated by the

magma to 1100 degree Kelvin or 19 kcal/mole. The high temperature water is an

explosive with the hot liquid water going to a water gas. The BKW steady state

detonation state has a peak pressure of 89 kilobars, a propagation velocity of 5900

meters/second and the water is compressed to 1.33 grams/cc.

The observed Krakatoa tsunami had a period of less than 5 minutes and wavelength of

less than 7 kilometers and thus rapidly decayed. The far field tsunami wave was

negligible. The air shock generated by the hydrovolcanic explosion propagated around

the world and coupled to the ocean resulting in the explosion being recorded on tide

gauges around the world.

Science of Tsunami Hazards, Vol. 24, No. 3, page 174 (2006)

INTRODUCTION

The Krakatoa volcanic explosion and its consequences are described in detail by

George Pararas-Carayannis in reference 1 and Simon Winchester in reference 2.

Krakatoa exploded August 27, 1883 obliterating 5 square miles of land and leaving a

crater 3.5 miles across and 200-300 meters deep. Thirty three feet high tsunami waves

hit Anjer and Merak, demolishing the towns and killing over 10,000 people. In Merak

the wave rose to 135 feet above sea level and moved 100 ton coral blocks up on the

shore. Tsunami waves swept over 300 coastal towns and villages killing 40,000 people.

The sea withdrew at Bombay, India and killed one person in Sri Lanka.

The tsunami was produced by a hydrovolcanic explosion and the associated shock

wave and pyroclastic flows.

A hydrovolcanic explosion is generated by the interaction of hot magma with ground

water. It is called Surtseyan after the 1963 explosive eruption off Iceland. The water

flashes to steam and expands explosively. Liquid water becoming water gas at constant

volume generates a pressure of 30,000 atmospheres.

The Krakatoa hydrovolcanic explosion was modeled using the full Navier-Stokes

AMR Eulerian compressible hydrodynamic code called SAGE with includes the high

pressure physics of explosions.

The observed Krakatoa tsunami had a period of less than 5 minutes and wavelength of

less than 7 kilometers and thus rapidly decayed. The far field tsunami wave was

negligible. The air shock generated by the hydrovolcanic explosion propagated around

the world and coupled to the ocean resulting in the explosion being recorded on tide

gauges around the world.

NUMERICAL MODELING

The compressible Navier-Stokes equations are described in reference 3 and 4 and

examples of many numerical solutions of complicated physical problems are described.

The compressible Navier-Stokes equations are solved by a high-resolution Godunov

differencing scheme using an adaptive grid technique described in reference 5.

The solution technique uses Continuous Adaptive Mesh Refinement (CAMR). The

decision to refine the grid is made cell-by-cell continuously throughout the calculation.

The computing is concentrated on the regions of the problem which require high

resolution.

Refinement occurs when gradients in physical properties (density, pressure,

temperature, material constitution) exceed defined limits, down to a specified minimum

cell size for each material. The mesh refinement is described in detail in reference 3.

Much larger computational volumes, times and differences in scale can be simulated

than possible using previous Eulerian techniques such as those described in reference 4.

The original code was called SAGE. A later version with radiation is called RAGE.

A recent version with the techniques for modeling reactive flow described in reference 3

is called NOBEL. It was used for the modeling of hydrovolcanic explosions described in

this paper.

Some of the remarkable advances in fluid physics using the SAGE code have been the

modeling of Richtmyer-Meshkov and shock induced instabilities described in references

Science of Tsunami Hazards, Vol. 24, No. 3, page 175 (2006)

6 and 7. It was used for modeling the Lituya Bay impact landslide generated tsunami

and water cavity generation described in references 8 and 9. NOBEL/SAGE/RAGE were

used to model the generation of water cavities by projectiles and explosions and the

resulting water waves in reference 10. The codes were used to model asteroid impacts

with the ocean and the resulting tsunami waves in references 11 and 12.

The codes can describe one-dimensional slab or spherical geometry, two-dimensional

slab or cylindrical geometry, and three-dimensional Cartesian geometry.

Because modern supercomputing is currently done on clusters of machines containing

many identical processors, the parallel implementation of the code is very important. For

portability and scalability, the codes use the Message Passing Interface (MPI). Load

leveling is accomplished through the use of an adaptive cell pointer list, in which newly

created daughter cells are placed immediately after the mother cells. Cells are

redistributed among processors at every time step, while keeping mothers and daughters

together. If there are a total of M cells and N processors, this technique gives nearly

(M / N) cells per processor. As neighbor cell variables are needed, the MPI gather/scatter

routines copy those neighbor variables into local scratch memory.

The calculations described in this paper were performed on IBM NetVista and

ThinkPad computers and did not require massive parallel computers.

The codes incorporate multiple material equations of state (analytical or SESAME

tabular). Every cell can in principle contain a mixture of all the materials in a problem

assuming that they are in pressure and temperature equilibrium.

As described in reference 4, pressure and temperature equilibrium is appropriate only

for materials mixed molecularly. The assumption of temperature equilibrium is

inappropriate for mixed cells with interfaces between different materials. The errors

increase with increasing density differences. While the mixture equations of state

described in reference 4 would be more realistic, the problem is minimized by using fine

numerical resolution at interfaces. The amount of mass in mixed cells is kept small

resulting in small errors being introduced by the temperature equilibrium assumption.

Very important for hydrovolcanic explosions, water cavity collapse and the resulting

water wave history is the capability to initialize gravity properly, which is included in the

code. This results in the initial density and initial pressure changing going from the

atmosphere at 2 kilometers altitude down to the ocean surface. Likewise the water

density and pressure changes correctly with ocean depth.

HYDROVOLCANIC MODEL

A hydrovolcanic explosion is generated by the interaction of hot magma with ground

water. It is called Surtseyan after the 1963 explosive eruption off Iceland. The water

flashes to steam and expands explosively. Liquid water becoming water gas at constant

volume generates a pressure of 30,000 atmospheres.

The Krakatoa hydrovolcanic explosion was modeled using the full Navier-Stokes

AMR Eulerian compressible hydrodynamic code called SAGE with includes the high

pressure physics of explosions.

Science of Tsunami Hazards, Vol. 24, No. 3, page 176 (2006)

The water in the hydrovolcanic explosion was described as liquid water heated by the

magma to 1100 degree Kelvin or 19 kcal/mole. The high temperature water is an

explosive with the hot liquid water going to a water gas. The BKW steady state

detonation state described in reference 4 has a peak pressure of 89 kilobars, a propagation

velocity of 5900 meters/second and the water is compressed to 1.33 grams/cc.

THE KRAKATOA MODEL

The island of Krakatoa today and before 1883 are shown in Figure 1.

Figure 1. Maps of Krakatoa today and before 1883.

It was modeled in two-dimensions as a spherical island 200 meters high above the

ocean level and 3 kilometers in radius tapering down to ocean level by 4 kilometers as

shown in Figure 2. The ocean was 100 meters deep and extended in the rock under the

island. The lava was initially assumed to interact with the water in the center of the

island in a 500 meter radius hot spot region. The propagating hydrovolcanic explosion

propagated outward at about 5900 meters per second and at a constant volume pressue of

about 30,000 atmospheres as shown in Figure 3.

Science of Tsunami Hazards, Vol. 24, No. 3, page 177 (2006)

Figure 2. The spherical model for the Krakatoa hydrovolcanic explosion.

Figure 3. The propagating hydrovolcanic explosion.

Science of Tsunami Hazards, Vol. 24, No. 3, page 178 (2006)

The expansion of the hydrovolcanic explosion is shown in Figures 4 and 5 at various

times up to 10 seconds as density picture plots.

Figure 4. The density profile at various times for the hydrovolcanic explosion of

Krakatoa.

Figure 5. The density profile at later times for the hydrovolcanic explosion

of Krakatoa.

Science of Tsunami Hazards, Vol. 24, No. 3, page 179 (2006)

The velocity contour picture plots in the X-direction are shown in Figure 6. The

propagation of the shock wave in the basalt below the island, the basalt above sea level,

the water and in the air is shown.

Figure 6. The velocity profiles in the horizontal or X-Direction at various times.

The water wave profiles at 4, 5, and 8 kilometers are shown in Figure 7. The wave

outside the hydrovolcanic explosion at 4 km is 130 meters high and decays to 48 meters

by 5 kilometers and to 7.5 meters at 8 kilometers.

Figure 7. The water wave profiles as a function of time at 4, 5 and 8 km.

Science of Tsunami Hazards, Vol. 24, No. 3, page 180 (2006)

The states of the water at 1.5 kilometers in the middle of the hydrovolcanic explosion of

the water reached pressures greater than 25,000 bars and expanded to altitudes greater

than 2 kilometers and drove the Krakatoa island basalt to altitudes greater than 2

kilometers. Perhaps the hydrovolcanic explosion looked something like 1946 Bikini

nuclear explosion shown in Figure 8 without the warships. The Baker shot was a 21

kiloton device fired at 27 meter depth in the ocean. The Krakatoa event released 150-200

megatons.

Figure 8. The 1946 Bikini Atomic Explosion.

CONCLUSIONS

A fully-compressible reactive hydrodynamic model for the process of hydrovolcanic

explosion of liquid water to steam at constant volume and pressures of 30,000

atmospheres has been applied to the explosion of Krakatoa in 1883. The idealized

spherical geometry exhibits the general characteristics observed including the destruction

of the island and the projection of the island into high velocity projectiles that travel into

the high upper atmosphere above 2 kilometers. A high wall of water is formed that is

initially higher than 100 meters driven by the shocked water, basalt and air. The initial

wave period of about 30 seconds and the rapid decay of the water wave suggests that the

hydrovolcanic explosion in the calculation was less than in the Krakatoa explosion. The

idealized 2-D geometry needs to be replaced with a realistic 3-D one. The

hydrovolcanic process needs to involve a more accurate description of the water filled

porous basalt layer where the hydrovolcanic explosion occurs.

Science of Tsunami Hazards, Vol. 24, No. 3, page 181 (2006)

The contributions of Dr. George Pararas-Carayannis are gratefully acknowledged.

REFERENCES

1. George Pararas-Carayannis, “Near and Far-Field Effects of Tsunamis Generated by the

Paroxysmal Eruptions, Explosions, Caldera Collapses and Massive Slope Failures of the

Krakatau Volcano in Indonesia on August 26-27, 1883,” Science of Tsunami Hazards,

Vol. 21, No. 4, pp 191-2l1 (2003).

2. Simon Winchester, Krakatoa, Harper Collins Publishers, New York, NY (2003)

3. Charles L. Mader, Numerical Modeling of Water Waves- Second Edition, CRC

Press, Boca Raton, Florida (2004).

4. Charles L. Mader, Numerical Modeling of Explosives and Propellants, CRC Press,

Boca Raton, Florida (1998).

5. M. L. Gittings, “1992 SAIC's Adaptive Grid Eulerian Code,” Defense Nuclear

Agency Numerical Methods Symposium, pp. 28-30 (1992).

6. R. L. Holmes, G. Dimonte, B. Fryxell, M. L. Gittings, J. W. Grove, M. Schneider, D.

H. Sharp, A. L. Velikovich, R. P. Weaver and Q. Zhang, “Richtmyer-Meshkov Instability

Growth: Experiment, Simulation and Theory,” Journal of Fluid Mechanics, Vol. 9, pp.

55-79 (1999).

7. R. M. Baltrusaitis, M. L. Gittings, R. P. Weaver, R. F. Benjamin and J. M. Budzinski,

“Simulation of Shock-Generated Instabilities,” Physics of Fluids, Vol. 8, pp. 2471-2483

(1996).

8. Charles L. Mader, “Modeling the 1958 Lituya Bay Tsunami,” Science of Tsunami

Hazards, Vol. 17, pp. 57-67 (1999).

9. Charles L. Mader, “Modeling the 1958 Lituya Bay Mega-Tsunami, II ,” Science of

Tsunami Hazards, Vol. 20, pp. 241-250 (2002).

10. Charles L. Mader and Michael L. Gittings, “Dynamics of Water Cavity Generation,”

Science of Tsunami Hazards, Vol. 21, pp. 91-118 (2003).

11. Galen Gisler, Robert Weaver, Michael L. Gittings and Charles Mader, “Two- and

Three-Dimensional Simulations of Asteroid Ocean Impacts,” Science of Tsunami

Hazards, Vol. 21, pp. 119-134 (2003).

12. Galen Gisler, Robert Weaver, Michael L. Gittings and Charles Mader, “Two- and

Three-Dimensional Asteroid Impact Simulations,” Computers in Science and

Engineering (2004).

Science of Tsunami Hazards, Vol. 24, No. 3, page 182 (2006)

Investigation of physical issues of the initial conditions of free water surface due to underwater disturbances on the basis of SPH numerical simulation of the phenomenon

Article

Full-text available

Feb 2019

The current paper discusses the physical impacts of the various initial boundary conditions of the free surface of a waterbody on the initiation and propagation characteristics of water waves due to the underwater perturbations. Differences between traditional point of view and applied numerical method in this paper for exertion the initial conditions of the generated waves by surface deformation were surveyed in the Lagrangian domain vs. Eulerian. In this article, the smoothed-particle hydrodynamics (SPH) technique was applied for simulating of wave generation process using initial boundary condition of water surface deformation through utilizing DualSPHysics numerical code and comparing the modeling results with recorded data. As a distinct approach, we studied the effects of discrete water particles on properties of produced surface waves by using the Lagrangian analytical capability of SPH model. Illustrative compatibility on simulation results with experimental data proves that meshless techniques such as applied in DualSPHysics software can reproduce physical properties of the event very well, and this is a suitable alternative to existing classical approaches for prediction of shock occurrences with nonlinear behavior such as generated surface water waves by underwater disturbance. Besides, the waveforms and their characteristics behave more realistic by considering the thrown upward water mass which was not directly considered in old formula and theories. The results of numerical modeling indicated rational agreement between numerical and empirical data proving that a complicated nonlinear phenomenon could be predicted by an SPH model which modified initial boundary conditions were supposed into the model with actual assumptions.

A Review of Tsunamis Generated by Volcanoes (TGV) Source Mechanism, Modelling, Monitoring and Warning Systems

Article

Full-text available

Jun 2024
PURE APPL GEOPHYS

Tsunamis generated by volcanic eruptions have risen to prominence since the December 2018 tsunami generated by the flank collapse of Anak Krakatau during a moderate eruption and then the global tsunami generated by the explosive eruption of the Hunga volcano in the Tongan Archipelago in January 2022. Both events cause fatalities and highlight the lack in tsunami warning systems to detect and warn for tsunamis induced by volcanic mechanisms. Following the Hunga Tonga—Hunga Ha’apai eruption and tsunami, an ad hoc working group on Tsunamis Generated by Volcanoes was formed by the Intergovernmental Oceanographic Commission of UNESCO. Volcanic tsunamis differ from seismic tsunamis in that there are a wide range of source mechanisms that can generate the tsunamis waves and this makes understanding, modelling and monitoring volcanic tsunamis much more difficult than seismic tsunamis. This paper provides a review of both the mechanisms behind volcanic tsunamis and the variety of modelling techniques that can be used to simulate their effects for tsunami hazard assessment and forecasting. It gives an example of a volcanic tsunami risk assessment undertaken for Stromboli, outlines the requirement of volcanic monitoring to warn for tsunami hazard and provides examples of volcanic tsunami warning systems in Italy, the Hawaiian Island (USA), Tonga and Indonesia. The paper finishes by highlighting the need for implementing monitoring and warning systems for volcanic tsunamis for locations with submarine volcanoes or near-shore volcanoes which could potentially generate tsunamis.

A Review of Historical Volcanic Tsunamis: A New Scheme for a Volcanic Tsunami Monitoring System

Article

Full-text available

Feb 2024

Tsunami monitoring and early warning systems are mainly established to deal with seis-mogenic tsunamis generated by sudden seafloor fault displacement. However, a global tsunami triggered by the 2022 Tonga volcanic eruption promoted the need for tsunami early warning and hazard mitigation of non-seismogenic tsunamis in coastal countries. This paper studied the spatiotem-poral distribution characteristics of historical volcanic tsunamis and summarized high-risk areas of volcanic tsunamis. The circum southwestern Pacific volcanic zone, including the Sunda volcanic belt and the Indo-Australian plate, is a concentrated area of active volcanoes and major volcanic tsunamis. In addition, the challenges associated with adapting seismogenic tsunami techniques for use in the context of volcanic tsunamis were elucidated. At the same time, based on historical records and post-disaster surveys, typical historical volcanic tsunami events and involved mechanisms were summarized. The results show that a majority of volcanic tsunamis may involve multiple generation mechanisms, and some mechanisms show geographical distribution characteristics. The complexity of volcanic tsunami mechanisms poses challenges to tsunami early warning by measuring tsunami sources to evaluate the possible extent of impact, or using numerical modeling to simulate the process of a tsunami. Therefore, a concise overview of the lessons learned and the current status of early warning systems for volcanic tsunamis was provided. Finally, a conceptual scheme of monitoring systems for volcanic tsunamis based on historical volcanoes, real-time volcanic eruption information and sea level data, as well as remote sensing images, was presented.

Progress in Tsunami Science: Toward an Improved Integration of Hydrodynamical Modeling and Geomorphic Field Evidence

Article

Full-text available

May 2022

Risks posed by sea-level rise and cyclones are becoming more prevalent along the world’s coastlines. In recent years, tsunamis have had devastating impacts on communities in different ocean basins. Although storms and tsunamis can be clearly distinguished when they occur in the present, this does not apply to the past, from which only their traces in the form of sedimentary or geomorphologic features provide clues about their occurrence. Following a short review of research on tsunamis from the last decades, this study uses the example of coastal boulder deposits to highlight where knowledge gaps exist. This report focuses on the spatial distribution of sediment patterns and how these may provide clues to the transport processes. However, the history of these deposits and related sea-level records during the same time span must also be recorded and contextualized. Theoretical modeling results without including these parameters will remain fuzzy, if not inaccurate. This contribution points to the need for consideration of both data and nature’s reality (which are complementary and interdependent) in this field.

Field Survey and Numerical Modelling of the December 22, 2018 Anak Krakatau Tsunami

Article

Full-text available

Jun 2020
PURE APPL GEOPHYS

On December 22, 2018, the eruption and flank collapse of the Anak Krakatau volcano generated a tsunami in the Sunda Strait causing catastrophic damage to uninhabited coastlines proximal to the source. Along the heavily populated shores of Banten and Lampung provinces in Java and Sumatra, tsunami waves caused severe damage, extensive inundation and more than 430 deaths. An international tsunami survey team (ITST) deployed 6 weeks after the event documented the tsunami effects including runup heights, flow depths and inundation distances, as well as sediment deposition patterns and impacts on infrastructure and the natural environment. The team also interviewed numerous eyewitnesses and educated residents about tsunami hazards. This ITST was the first to visit and document the extreme tsunami effects on the small islands in the Sunda Strait closest to Anak Krakatau (Rakata, Panjang, Sertung, Sebesi and Panaitan). Along the steep slopes of Rakata and Sertung islands, located less than 5 km from and facing directly towards the southwest flank of Anak Krakatau, all of the dense coastal vegetation was stripped to bare earth up to elevations of more than 80 m, while on the northeast tip of Sertung Island, facing away from the source, a single tree remained standing after flow depths of > 11 m above ground struck there. The runup distributions on the islands encircling Anak Krakatau highlight the directivity of the tsunami source suggesting that the collapse occurred towards the southwest. This manifested as tsunami runup of < 10 m on Sebesi Island, located 15 km northeast of the source, contrasting with tsunami flow heights > 10 m that stripped away coastal forests to bare rock for up to 400 m inland in the Ujung Kulon National Park, located 50 km to the south-southwest. Inundation and damage were mostly limited to within 400 m of the shoreline, likely the result of the relatively short wavelengths caused by the landslide generated tsunami. A significant variation in tsunami impact was observed along the shorelines of the Sunda Strait, with runup heights rapidly decreasing with distance from the inferred tsunami source. To model the event we applied a hot-start initial condition that roughly reproduced the measured tsunami runup heights along Rakata and Sertung. The waveforms were then propagated through the Sunda Straight using a Boussinesq-type wave model. The results showed a good fit to the observed heights along the Java and Sumatra coastlines, the northern coast of Panaitan Island and Ujung Kulon Nation Park. The model also produced an acceptable fit to the observed amplitudes at tide gauges. Despite the regional volcanic and tsunamigenic history of the region, and 6-months of eruptive activity prior to the event, the tsunami largely caught the local population off guard. This further highlights the need for community-based education and awareness programs as essential to save lives in locales at risk from locally generated tsunamis.

The Physics of Tsunami Formation by Sources of Nonseismic Origin

Chapter

Jan 2009

The physics is described of tsunami formation by sources of nonseis-mic origin: landslides, volcanic eruptions, meteorological causes and cosmic bodies falling into the ocean. Short descriptions are given of certain remarkable historical events (with the exception of cosmogenic tsunamis). Approaches to the mathematical description of tsunami generation by these sources are expounded. Basic regularities, relating parameters of a source and of the tsunami wave generated by it are presented.

The Physics of Tsunami Formation by Sources of Nonseismic Origin

Chapter

Jan 2016

The physics is described of tsunami formation by sources of nonseismic origin: landslides, volcanic eruptions, meteorological causes, and cosmic bodies falling into the ocean. Short descriptions are given of certain remarkable historical events (with the exception of cosmogenic tsunamis). Approaches to the mathematical description of tsunami generation by these sources are expounded. Basic regularities, relating parameters of a source and of the tsunami wave generated by it are presented.

Physics of Tsunamis

Article

Jan 2009

There has been significant progress in tsunami research, monitoring and mitigation within the last decade. This book summarizes the state-of-the-art knowledge on tsunamis. It presents a comprehensive overview of tsunamis, seaquakes and other catastrophic ocean phenomena. It describes up-to-date models of tsunamis generated by a submarine earthquake, landslide, volcanic eruption, meteorites impact, and moving atmospheric pressure inhomogeneities. Models of tsunami propagation and run-up are also discussed. The book investigates methods of tsunami monitoring including satellite altimetry and the study of paleotsunamis. Non-linear phenomena in tsunami source are discussed in the context of their contribution to the wave amplitude and intensification of the vertical exchange in ocean. The book is intended for scientists, researchers and specialists in oceanography, geophysics, seismology, hydro-acoustics, geology, geomorphology, including the engineering and insurance industries. © 2009 Springer Science + Business Media B.V. All Rights Reserved.

Numerical study on three-dimensional waves produced by a bottom jet

Article

Mar 2015
APPL OCEAN RES

The eruption of an underwater volcano can initiate the disturbances of the sea surface and subsequently generate a group of outward-propagating tsunamis. The theme of this study is to introduce a three-dimensional (3D) fully nonlinear wave model for the simulation of wave motions induced by a bottom jet. A boundary-fitted coordinate system is utilized to conveniently adjust grids according to the transient moving free surface. The governing Laplace equation of the velocity potential is solved by an implicit finite-difference scheme while a mixed explicit/implicit iteration procedure is applied to solve the free-surface boundary conditions. In addition, a set of generalized Boussinesq equations are solved for comparison with the fully nonlinear model. Good agreements in comparisons with the existing numerical and analytical solutions are achieved for cases investigated. Waves induced by three types of bottom jets: namely (1) sudden eruption, (2) initial transient, and (3) periodic transient are discussed in this paper. For the case of sudden erupted jet, a system of 3D outgoing waves as the cylindrical wave pattern are presented and discussed. For the initial transient types, it shows the transition in the incipient stage has a great influence on the initial rising of the water surface and the induced leading waves. Furthermore, an interesting up-down phenomenon in the center of disturbed free surface due to the type of periodic jet is revealed.

A probabilistic tsunami hazard assessment for Indonesia

Article

Full-text available

Nov 2014

Probabilistic hazard assessments are a fundamental tool for assessing the threats posed by hazards to communities and are important for underpinning evidence-based decision-making regarding risk mitigation activities. Indonesia has been the focus of intense tsunami risk mitigation efforts following the 2004 Indian Ocean tsunami, but this has been largely concentrated on the Sunda Arc with little attention to other tsunami prone areas of the country such as eastern Indonesia. We present the first nationally consistent probabilistic tsunami hazard assessment (PTHA) for Indonesia. This assessment produces time-independent forecasts of tsunami hazards at the coast using data from tsunami generated by local, regional and distant earthquake sources. The methodology is based on the established monte carlo approach to probabilistic seismic hazard assessment (PSHA) and has been adapted to tsunami. We account for sources of epistemic and aleatory uncertainty in the analysis through the use of logic trees and sampling probability density functions. For short return periods (100 years) the highest tsunami hazard is the west coast of Sumatra, south coast of Java and the north coast of Papua. For longer return periods (500–2500 years), the tsunami hazard is highest along the Sunda Arc, reflecting the larger maximum magnitudes. The annual probability of experiencing a tsunami with a height of > 0.5 m at the coast is greater than 10% for Sumatra, Java, the Sunda islands (Bali, Lombok, Flores, Sumba) and north Papua. The annual probability of experiencing a tsunami with a height of > 3.0 m, which would cause significant inundation and fatalities, is 1–10% in Sumatra, Java, Bali, Lombok and north Papua, and 0.1–1% for north Sulawesi, Seram and Flores. The results of this national-scale hazard assessment provide evidence for disaster managers to prioritise regions for risk mitigation activities and/or more detailed hazard or risk assessment.

Modeling the 1958 Lituya Bay Mega-Tsunami

Article

Full-text available

Jan 2001

Charles Mader

Modeling the 1958 Lituya Bay Mega-tsunami, II

Article

Full-text available

Jan 2002

Lituya Bay, Alaska is a T-Shaped bay, 7 miles long and up to 2 miles wide. The two arms at the head of the bay, Gilbert and Crillon Inlets, are part of a trench along the Fairweather Fault. On July 8, 1958, an 7.5 Magnitude earthquake occurred along the Fairweather fault with an epicenter near Lituya Bay.A mega-tsunami wave was generated that washed out trees to a maximum altitude of 520 meters at the entrance of Gilbert Inlet. Much of the rest of the shoreline of the Bay was denuded by the tsunami from 30 to 200 meters altitude.In the previous study it was determined that if the 520 meter high run-up was 50 to 100 meters thick, the observed inundation in the rest of Lituya Bay could be numerically reproduced. It was also concluded that further studies would require full Navier-Stokes modeling similar to those required for asteroid generated tsunami waves.During the Summer of 2000, Hermann Fritz conducted experiments that reproduced the Lituya Bay 1958 event. The laboratory experiments indicated that the 1958 Lituya Bay 524 meter run-up on the spur ridge of Gilbert Inlet could be caused by a landslide impact.The Lituya Bay impact landslide generated tsunami was modeled with the full Navier- Stokes AMR Eulerian compressible hydrodynamic code called SAGE with includes the effect of gravity.

Modeling the 1958 Lituya Bay Mega-Tsunami

Article

Full-text available

Jan 1999

Charles Mader

Simulation of shock-generated instabilities

Article

Full-text available

Sep 1996

Direct 2-D numerical simulation of the fluid instability of a shock-accelerated thin gas layer shows flow patterns in agreement with experimental images. The Eulerian-based hydrodynamics code features Adaptive Mesh Refinement that allows the code to follow the vorticity generation and the complex flow resulting from the measured initial perturbations. These experiments and simulations are the first to address in quantitative detail the evolution of the Richtmyer–Meshkov instability in a thin fluid layer, and to show how interfluid mixing and vorticity production depend sensitively on initial perturbations in the layer.

Richtmyer-Meshkov instability growth: Experiment, simulation and theory

Article

Full-text available

Jun 1999
J FLUID MECH

Richtmyer–Meshkov instability is investigated for negative Atwood number and two-dimensional sinusoidal perturbations by comparing experiments, numerical simulations and analytic theories. The experiments were conducted on the NOVA laser with strong radiatively driven shocks with Mach numbers greater than 10. Three different hydrodynamics codes (RAGE, PROMETHEUS and FronTier) reproduce the amplitude evolution and the gross features in the experiment while the fine-scale features differ in the different numerical techniques. Linearized theories correctly calculate the growth rates at small amplitude and early time, but fail at large amplitude and late time. A nonlinear theory using asymptotic matching between the linear theory and a potential flow model shows much better agreement with the late-time and large-amplitude growth rates found in the experiments and simulations. We vary the incident shock strength and initial perturbation amplitude to study the behaviour of the simulations and theory and to study the effects of compression and nonlinearity.

Two-and three-dimensional simulations of asteroid ocean impacts

Article

Full-text available

Jan 2003

We have performed a series of two-dimensional and three-dimensional simulations of asteroid impacts into an ocean using the SAGE code from Los Alamos National Laboratory and Science Applications International Corporation. The SAGE code is a compressible Eulerian hydrodynamics code using continuous adaptive mesh refinement for following discontinuities with a fine grid while treating the bulk of the simulation more coarsely. We have used realistic equations of state for the atmosphere, sea water, the oceanic crust, and the mantle. In two dimensions, we simulated asteroid impactors moving at 20 km/s vertically through an exponential atmosphere into a 5 km deep ocean. The impactors were composed of mantle material (3.32 g/cc) or iron (7.8 g/cc) with diameters from 250m to 10 km. In our three-dimensional runs we simulated asteroids of 1 km diameter composed of iron moving at 20 km/s at angles of 45 and 60 degrees from the vertical. All impacts, including the oblique ones, produce a large underwater cavities with nearly vertical walls followed by a collapse starting from the bottom and subsequent vertical jetting. Substantial amounts of water are vaporized and lofted high into the atmosphere. In the larger impacts, significant amounts of crustal and even mantle material are lofted as well. Tsunamis up to a kilometer in initial height are generated by the collapse of the vertical jet. These waves are initially complex in form, and interact strongly with shocks propagating through the water and the crust. The tsunami waves are followed out to 100 km from the point of impact. Their periods and wavelengths show them to be intermediate type waves, and not (in general) shallow-water waves. At great distances, the waves decay as the inverse of the distance from the impact point, ignoring sea-floor topography. For all impactors smaller than about 2 km diameter, the impacting body is highly fragmented and its remains lofted into the stratosphere with the water vapor and crustal material, hence very little trace of the impacting body should be found for most oceanic impacts. In the oblique impacts, the initial asymmetry of the transient crater and crown does not persist beyond a tsunami propagation length of 50 km.

Numerical modeling of water waves. With CD-ROM

Article

Jun 2004

Charles Mader

Dynamics of Water Cavity Generation

Article

Jan 2003

The hypervelocity impact (1.25 to 6 km/sec) of projectiles into water has been studied at the University of Arizona by Gault and Sonett. They observed quite different behavior of the water cavity as it expanded when the atmospheric pressure was reduced from one to a tenth atmosphere. Above about a third of an atmosphere, a jet of water formed above the expanding bubble and a jet or “root” emerged below the bottom of the bubble.Similar results were observed by Kedrinskii at the Institute of Hydrodynamics in Novosibirsk, Russia when the water cavity was generated by exploding bridge wires with jets and roots forming for normal atmospheric pressure and not for reduced pressures.Earlier at the Los Alamos National Laboratory B. G. Craig, reported observing the formation of jets and roots while the gas cavity was expanding by bubbles generated by small spherical explosives detonated near the water surface.During the last decade a compressible Eulerian hydrodynamic code called SAGE has been under development by the Los Alamos National Laboratory and Science Applications International (SAIC) which has continuous adaptive mesh refinement (AMR) for following shocks and contact discontinuities with a very fine grid while using a coarse grid in smooth flow regions.A version of the SAGE code that models explosives called NOBEL has been used to model the experimental geometries of Sonett and of Craig. The experimental observations were reproduced as the atmospheric pressure was varied. When the atmospheric pressure was increased the difference between the pressure outside the ejecta plume above the water cavity and the decreasing pressure inside the water plume and cavity as it expanded resulted in the ejecta plume converging and colliding at the axis forming a jet of water proceeding above and back into the bubble cavity along the axis. The jet proceeding back thru the bubble cavity penetrates the bottom of the cavity and forms the root observed experimentally. The complicated bubble collapse and resulting cavity descent into deeper water was numerically reproduced.Now that a code is available that can describe the experimentally observed features of projectile interaction with the ocean, we have a tool that can be used to evaluate impact landslide, projectile or asteroid interactions with the ocean and the resulting generation of tsunami waves.

Numerical Modeling of Water Waves

Book