Tsunami waves. Denys DUTYKH 1. Centre de Mathématiques et de Leurs Applications English for scientists

Transcription

1 Tsunami waves Denys DUTYKH 1 1 Ecole Normale Supérieure de Cachan, Centre de Mathématiques et de Leurs Applications Denys.Dutykh@cmla.ens-cachan.fr English for scientists D. Dutykh (ENS Cachan) Tsunami waves English for scientists 1 / 33

2 Contents 1 General information on tsunamis Characteristics of tsunami waves Subduction zone Tsunami run-up 2 Tsunami wave modelling Approaches to generation Tsunami propagation simulations 3 Tsunami warning system Major players in tsunami world Directions for improvements D. Dutykh (ENS Cachan) Tsunami waves English for scientists 2 / 33

3 Contents 1 General information on tsunamis Characteristics of tsunami waves Subduction zone Tsunami run-up 2 Tsunami wave modelling Approaches to generation Tsunami propagation simulations 3 Tsunami warning system Major players in tsunami world Directions for improvements D. Dutykh (ENS Cachan) Tsunami waves English for scientists 2 / 33

4 Contents 1 General information on tsunamis Characteristics of tsunami waves Subduction zone Tsunami run-up 2 Tsunami wave modelling Approaches to generation Tsunami propagation simulations 3 Tsunami warning system Major players in tsunami world Directions for improvements D. Dutykh (ENS Cachan) Tsunami waves English for scientists 2 / 33

5 General information on tsunamis Definition of tsunami wave The origin of the word «tsunami» : tsu is harbour, nami is wave FIG.: in Kanji Scientific definition Surface gravity waves that occur in the ocean as the result of large-scale short-term perturbations such as underwater earthquakes, eruption or underwater volcanoes, submarine landslides, underwater explosions, rock and asteroid flows in the water and sometimes drastic changes of weather conditions D. Dutykh (ENS Cachan) Tsunami waves English for scientists 3 / 33

6 General information on tsunamis Definition of tsunami wave The origin of the word «tsunami» : tsu is harbour, nami is wave FIG.: in Kanji Scientific definition Surface gravity waves that occur in the ocean as the result of large-scale short-term perturbations such as underwater earthquakes, eruption or underwater volcanoes, submarine landslides, underwater explosions, rock and asteroid flows in the water and sometimes drastic changes of weather conditions D. Dutykh (ENS Cachan) Tsunami waves English for scientists 3 / 33

7 General information on tsunamis Hokusai s picture, IXX century D. Dutykh (ENS Cachan) Tsunami waves English for scientists 4 / 33

8 General information on tsunamis Characteristics of tsunami waves Quantitative characteristics Typical seismic tsunami in Indian or Pacific ocean parameter value Wavelength Amplitude Velocity in deep ocean Velocity at shallow water 100 km 50 cm 200 m s or 720 km h 20 m s Propagation velocity c = gh, where g : gravity acceleration, 9.8 m, s 2 H : total water depth D. Dutykh (ENS Cachan) Tsunami waves English for scientists 5 / 33

9 General information on tsunamis Characteristics of tsunami waves Quantitative characteristics Typical seismic tsunami in Indian or Pacific ocean parameter value Wavelength Amplitude Velocity in deep ocean Velocity at shallow water 100 km 50 cm 200 m s or 720 km h 20 m s Propagation velocity c = gh, where g : gravity acceleration, 9.8 m, s 2 H : total water depth D. Dutykh (ENS Cachan) Tsunami waves English for scientists 5 / 33

10 General information on tsunamis Characteristics of tsunami waves Life of a Tsunami - I General description Three phases of tsunami life Generation Propagation Run-up Difficult modelling It seems that one needs three different models for each phase of tsunami life. D. Dutykh (ENS Cachan) Tsunami waves English for scientists 6 / 33

11 General information on tsunamis Subduction zone Earthquake generation mechanism Underwater shallow event Subduction zone Is an area on Earth where two tectonic plates meet and move towards one another, with one sliding underneath the other and moving down into the mantle, at rates typically measured in centimeters per year. D. Dutykh (ENS Cachan) Tsunami waves English for scientists 7 / 33

12 General information on tsunamis Subduction zone Life of a Tsunami : generation Seismology/Hydrodynamics coupling Generation stages : Stress accumulation due to plate movement This process results in Earthquake which deforms seabed Seafloor pushes water column up and down This wave propagates under the force of gravitation D. Dutykh (ENS Cachan) Tsunami waves English for scientists 8 / 33

13 General information on tsunamis Subduction zone Life of a Tsunami : coastal regions Nonlinear transformations When tsunami approaches the coast : wave slows, since the depth becomes smaller wavelength decreases rapidly amplitude increases D. Dutykh (ENS Cachan) Tsunami waves English for scientists 9 / 33

14 General information on tsunamis Subduction zone Nonlinear wave transformations Amplitude raise and wave reflection illustration D. Dutykh (ENS Cachan) Tsunami waves English for scientists 10 / 33

15 General information on tsunamis Subduction zone Life of a Tsunami : run-up Final stage Definition of run-up : Runup is a measurement of the height of the water onshore observed above a reference sea level. Run-up is the most dangerous and devastating phase of tsunami. D. Dutykh (ENS Cachan) Tsunami waves English for scientists 11 / 33

16 General information on tsunamis Tsunami run-up Run-up pictures - I Location : Banda Aceh Northern Shore, Indonesia Before tsunami : D. Dutykh (ENS Cachan) Tsunami waves English for scientists 12 / 33

17 General information on tsunamis Tsunami run-up Run-up pictures - I Location : Banda Aceh Northern Shore, Indonesia After tsunami : D. Dutykh (ENS Cachan) Tsunami waves English for scientists 12 / 33

18 General information on tsunamis Tsunami run-up Run-up pictures - II Location : Gleebruk Village, Sri Lanka Before tsunami : D. Dutykh (ENS Cachan) Tsunami waves English for scientists 13 / 33

19 General information on tsunamis Tsunami run-up Run-up pictures - II Location : Gleebruk Village, Sri Lanka After tsunami : D. Dutykh (ENS Cachan) Tsunami waves English for scientists 13 / 33

20 General information on tsunamis Tsunami run-up Tsunami inundation videos - I Location : Koh Lanta, Thailand D. Dutykh (ENS Cachan) Tsunami waves English for scientists 14 / 33

21 General information on tsunamis Tsunami run-up Tsunami inundation videos - II Location : Koh Lanta, Thailand D. Dutykh (ENS Cachan) Tsunami waves English for scientists 15 / 33

22 Tsunami wave modelling Approaches to generation Why model tsunami generation? Motivation for our research Principal reasons Provide initial condition to numerous codes for tsunami propagation modelling Understand the main effects to take into account during the first minutes of tsunami Hydrodynamics/seismology coupling is not well understood at present moment D. Dutykh (ENS Cachan) Tsunami waves English for scientists 16 / 33

23 Tsunami wave modelling Approaches to generation Traditional approach Common practice in actual tsunami modelling Put coseismic displacements directly on the free surface and let it propagate : 1.2 Free surface z/h Sea bed y, km x, km D. Dutykh (ENS Cachan) Tsunami waves English for scientists 17 / 33

24 Tsunami wave modelling Approaches to generation Traditional approach Common practice in actual tsunami modelling Put coseismic displacements directly on the free surface and let it propagate : 1.2 Free surface z/h Sea bed y, km x, km D. Dutykh (ENS Cachan) Tsunami waves English for scientists 17 / 33

25 Tsunami wave modelling Approaches to generation Main drawbacks of traditional method The most obvious drawbacks We don t take into account : Initial velocity field is neglected u t=0 = 0 Dynamic character of the rupture as well as time characteristics of source are not taken into account D. Dutykh (ENS Cachan) Tsunami waves English for scientists 18 / 33

26 Tsunami wave modelling Approaches to generation Example of proper numerical generation Nonlinear shallow water equations D. Dutykh (ENS Cachan) Tsunami waves English for scientists 19 / 33

27 Tsunami wave modelling Approaches to generation Passive vs Active generation How large is error in translating sea-bed deformation onto free surface? Passive generation Deformation translated on free surface η(x, y, t) = 1 ζ(k, l) cos ωt e i(kx+ly) (2π) 2 dkdl, Active generation R 2 Bottom moves with Heaviside function η i (x, y, t) = 1 ζ(k, l)e i(kx+ly) (2π) 2 cosωt dkdl, cosh(mh) R 2 where ζ(k, l) is the Fourier transform of ζ(x, y), m := k 2 + l 2, ω 2 := gm tanh(mh). D. Dutykh (ENS Cachan) Tsunami waves English for scientists 20 / 33

28 Tsunami wave modelling Approaches to generation Recent publication on Tsunami s generation Comptes Rendus de l Académie des Sciences D. Dutykh (ENS Cachan) Tsunami waves English for scientists 21 / 33

29 Tsunami wave modelling Approaches to generation Ananymous referee report Comments from referee This manuscript addresses an extremely simple but extremely important problem having to do with the generation of waves (tsunami waves, for example) [...] While the paper is very simple mathematically, in my opinion it is very important to report on results such as these, both for reasons of good applied mathematics and for appropriate use by the general scientific community. I would recommend that this paper be accepted for the CRAS (although Mechanics might have been slightly more appropriate than Mathematics). FIG.: Min Chen D. Dutykh (ENS Cachan) Tsunami waves English for scientists 22 / 33

30 Tsunami wave modelling Tsunami propagation simulations Numerical simulation of wave propagation - I the 26 December 2004 event D. Dutykh (ENS Cachan) Tsunami waves English for scientists 23 / 33

31 Tsunami wave modelling Tsunami propagation simulations Numerical simulation of wave propagation - II the 26 December 2004 event D. Dutykh (ENS Cachan) Tsunami waves English for scientists 24 / 33

32 Tsunami warning system NOAA - I Tsunami research in USA D. Dutykh (ENS Cachan) Tsunami waves English for scientists 25 / 33

33 Tsunami warning system Major players in tsunami world NOAA - II Major players : Frank Gonzalez Frank Gonzalez PhD in physical oceanography, University of Hawaii, 1975 joined PMEL two years later Director Emeritus at NOAA/PMEL physical and technical aspects in PTWC D. Dutykh (ENS Cachan) Tsunami waves English for scientists 26 / 33

34 Tsunami warning system Major players in tsunami world NOAA - III Major players : Vasily Titov Vasily Titov PhD at Novosibirsk, Russia Chief Scientist at NOAA/PMEL Researcher at University of Washington PTWS : numerical modelling of Tsunami, code MOST D. Dutykh (ENS Cachan) Tsunami waves English for scientists 27 / 33

35 Tsunami warning system Major players in tsunami world Early detection of tsunamis Tsunameter network Basic ideas Seismic waves propagate 20 times faster than tsunamis Seismometer data inversion gives rough characteristics of an Earthquake Tsunami propagation is calculated on computers Recommendations are sent to dangerous places Tsunameter network Before sending an alarm signal the computation results are compared to measurements One false alarm signal in Hawaii costs about $70M D. Dutykh (ENS Cachan) Tsunami waves English for scientists 28 / 33

36 Tsunami warning system Major players in tsunami world Tsunami warning system in Pacific ocean Principles of working D. Dutykh (ENS Cachan) Tsunami waves English for scientists 29 / 33

37 Tsunami warning system Major players in tsunami world Drawbacks the 15 November 2006 earthquake at Kuril Islands Recent article in «Nature» California caught off guard by tsunami California did not receive alarm signal Only a few first waves were computed The most important wave was the 7th Fortunately no casualties! D. Dutykh (ENS Cachan) Tsunami waves English for scientists 30 / 33

38 Tsunami warning system Directions for improvements Indian ocean tsunami warning system Indonesia/German collaboration D. Dutykh (ENS Cachan) Tsunami waves English for scientists 31 / 33

39 Tsunami warning system Directions for improvements July 17, 2006 Java Earthquake and Tsunami Timeline 08h :19 Earthquake occurs 08h :25 PTWC computers detect seismic signals and alert analysts Preliminary Rapid Earthquake Analysis 08h :31 Report from Matsushiro : M = 7.0, 9.36S, E, 30Km 08h :33 Tsunami Travel Time Computations (point source) 08h :36 PTWC Bulletin N1 - Local Tsunami Watch : Indonesia + Australia 08h :39-43 PTWC calls Indonesia to confirm receipt (phones busy) D. Dutykh (ENS Cachan) Tsunami waves English for scientists 32 / 33

40 Tsunami warning system Directions for improvements European program of Tsunami research TRANSFER project D. Dutykh (ENS Cachan) Tsunami waves English for scientists 33 / 33