Skip to main content
Log in

Hydrodynamic aspects of tsunami wave motion: a review

  • Published:
Ocean Dynamics Aims and scope Submit manuscript

Abstract

Since the 2004 Indian Ocean tsunami and particularly after the 2011 Tohuku tsunami, there has been a significant increase of computer simulation using real-time data; however, there are evidences of failures in pre-disaster preparedness. The scientific challenges to mitigate tsunami hazards rely heavily on understanding the hydrodynamics of the motion. The problem with tsunami is that it grows beyond the natural boundaries of generation and covers many oceans confronting different physical parameters which not only makes it a real global event but also enhances the complexity of the event. In this article, one, the underlying physical phenomena of tsunami motion starting from generation to evolution is identified. Two, the linear and non-linear studies of wave propagation and the effect of several oceanic parameters to the basic motion are highlighted. Three, considering the importance of tsunami wave runup, its research both at the theoretical and computational level is thoroughly explained. Four, although the majority of tsunamis are earthquake or landslide generated, there are instances of tsunamis generated by other sources; a brief review in this regard is provided. Five, the importance of benchmark problems for developing modelling tools is imperative; an attempt is made to underscore the obstacles faced while implementing the new improvements in hazard mitigation. Six, new research avenues are explored based on lessons learned over the years.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Abdolali A, Kirby JT, Bellotti G (2015) Depth-integrated equation for hydro-acoustic waves with bottom damping. J Fluid Mech 766(R1):1–13

    Article  Google Scholar 

  • Ammon CJ, Ji C, Thio HK, Robinson D, Ni S, Hjorleifsdottir V, Kanamori H, Lay T, Das S, Helmberger D, Ichinose G, Polet J, Wald D (2005) Rupture process of the 2004 Sumatra-Andaman earthquake. Science 308:1133–1139

    Article  Google Scholar 

  • Ammon CJ, Kanamori H, Lay T, Velasco AA (2006) The 17 July 2006 Java tsunami earthquake. Geophys Res Letter 33:L24308

    Article  Google Scholar 

  • Arcas D, Titov V (2006) Sumatra tsunami: lessons from modeling. Surv Geophys 27:679–705

    Article  Google Scholar 

  • Bandyopadhyay A (2013) Identification of forerunners and transmission of energy to tsunami waves generated by instanteneous ground motion on a non-uniformly sloping beach. Int J Geosci 4:454–460

    Article  Google Scholar 

  • Bandyopadhyay A, Mandal A (2014) Energy transmission to long waves generated by instantaneous ground motion on a beach. J Ocean Mechan Aerospace 17-23:6

    Google Scholar 

  • Bernard EN, Robinson AR (2009) The Sea, 15. Harvard University Press, Cambridge

    Google Scholar 

  • Bernard E, Titov V (2015) Evolution of tsunami warning systems and products. Phill Trans R Soc A 373:20140371

    Article  Google Scholar 

  • Bilham R (2005) A Flying Start, Then a slow slip. Science 308:1126–1127

    Article  Google Scholar 

  • Bryant E (2014) Tsunami the underrated Hazard, 3rd edn. Springer Int Publ, Switzerland, pp 19–32

    Google Scholar 

  • Carrier GF, Greenspan HP (1958) Water waves of finite amplitude on a sloping beach. J Fluid Mech 4:97–109

    Article  Google Scholar 

  • Carrier GF (1966) Gravity waves on water of variable depth. J Fluid Mech 24:641–659

    Article  Google Scholar 

  • Carrier GF, Noiseux CF (1983) The reflection of obliquely incident tsunamis. J Fluid Mech 133:147–160

    Article  Google Scholar 

  • Carrier GF, Wu TT, Yeh H (2003) Tsunami run-up and draw-down on a plane beach. J Fluid Mech 475:79–99

    Article  Google Scholar 

  • Carrier GF, Yeh H (2005) Tsunami propagation from a finite source. CMES 10:113–121

    Google Scholar 

  • Choi BH, Pelinovsky E, Kim DC, Didenkulova I, Woo SB (2008) Two and three dimensional computation and solitary wave runup on non-plane beach. Nonlin Processes Geophys 15:489–502

    Article  Google Scholar 

  • Collins A (2009) Early warning: a people-centered approach to early warning systems and the last mile. In: World Disasters Report 2009. International Federation Red Cross and Red Crescent Societies, Switzerland, pp 39–67

  • Constantin A, Johnson RS (2016) Current and future prospects for the application of systematic theoretical methods to the study of problems in physical oceanography. Phys Lett A 380:3007–3012

    Article  Google Scholar 

  • Craig W, Guyenne P, Sulem C (2009) Water waves over a random bottom. J Fluid Mech 640:79–107

    Article  Google Scholar 

  • Degueldre H, Metzger JJ, Geisel T, Fleischmann R (2015) Random focusing of tsunami waves. Nat Phys 12:259–262

    Article  Google Scholar 

  • Dutykh D, Dias F, Kervella Y (2006) Linear theory of wave generation by a moving bottom. Comptes Rendus Mathematique 343:499–504

    Article  Google Scholar 

  • Fukao Y, Sandanbata O, Sugioka H, Ito A, Shiobara H, Watada S, Satake K (2018) Mechanism of the 2015 volcanic tsunami earthquake near Torishima. Japan Sci Adv 4:1–10

    Google Scholar 

  • Geist EL, Bilek SL, Arcas D, Titov VV (2006) Differences in tsunami generation between the December 26, 2004 and March 28, 2005 Sumatra earthquakes. Earth Planets Space 58:185–193

    Article  Google Scholar 

  • Grilli ST, Tappin DR, Carey S, Watt SFL, Ward SN, Grilli AR, Engwell SL, Zhang C, Kirby JT, Schambach L, Muin M (2019) Modelling of the tsunami from the December 22, 2018 lateral collapse of Anak Krakatau volcano in the Sunda Straits, Indonesia. Scientif Rep Nat Res 9:11946

    Google Scholar 

  • Grimshaw R, Yuan C (2016) Depression and elevation tsunami waves in the framework of the Korteweg-de Vries equation. Nat Hazards 84:S493–S511

    Article  Google Scholar 

  • Gusiakov VK (2009) The Sea, 15. In: Bernard EN, Robinson AR (eds). Harvard University Press, Cambridge, pp 1–30

  • Hall JV, Watts JW (1953) Laboratory investigation of the vertical rise of solitary waves on impermeable slopes. Beach Erosion Board USACE Tech Memo 33:14

    Google Scholar 

  • Hughes SA (2004) Estimation of wave run-up on smooth, impermeable slopes using the wave momentum flux parameter. Coast Eng 51:1085–1104

    Article  Google Scholar 

  • Huppert HE, Sparks RSJ (2006) Extreme natural hazards: population growth, globalization and environmental change. Phil Trans R Soc A 364:1875–1888

    Article  Google Scholar 

  • Jinadasa S (2008) Interaction of tsunami wave propagation with coastal bathymetry and geo-morphology; a case study in Sri Lanka, NARA

  • Kadri U, Akylas TR (2016) On resonant triad interactions of acoustic–gravity waves. J Fluid Mech 788(R1):1–12

    Article  Google Scholar 

  • Kadri U, Crivelli D, Parsons W, Colbourne B, Ryan A (2017) Rewinding the waves: tracking underwater signals to their source. Scientif Rep 7:1–12

    Google Scholar 

  • Kadri U, Stiassnie M (2013) Generation of an acoustic–gravity wave by two gravity waves and their subsequent mutual interaction. J Fluid Mech 735(R6):1–9

    Google Scholar 

  • Kanoglu U, Synolakis CE (1998) Long wave runup on piecewise linear topographies. J Fluid Mech 374:1–28

    Article  Google Scholar 

  • Kanoglu UTVV, Aydin B, Moore C, Stefanakis TS, Zhou H, Spillane M, Synolakis CE (2013) Focusing of long waves with finite crest over constant depth. Proc R Soc A 469:1–20

    Article  Google Scholar 

  • Kanoglu U, Titov VV, Bernard EN, Synolakis CE (2015) Tsunamis: bridging science, engineering and society. Phil Trans R Soc A 373:20140369

    Article  Google Scholar 

  • Keller JB, Keller HB (1964) Water wave run-up on a beach, ONR Research Report NONR-3828 (00). Department of The Navy, Washington

    Google Scholar 

  • Kervella Y, Dutykh D, Dias F (2007) Comparison between three dimensional linear and nonlinear tsunami generation models. Theoret Comput Fluid Dynam 21:245–269

    Article  Google Scholar 

  • Kirby JT, Shi F, Tehranirad B, Harris JC, Grilli ST (2013) Dispersive tsunami waves in the ocean: model equations and sensitivity to dispersion and Coriolis effects. Ocean Model 62:39–55

    Article  Google Scholar 

  • Kremer et al (2017) Possible climate preconditioning on submarine landslides along a convergent margin. Nankai Trough (NE Pacific),Prog Earth Planet Sci 4:20

    Article  Google Scholar 

  • Levin B, Nosov M (2009) Physics of tsunamis. In: Propagation of a Tsunami in the Ocean and Its Interaction with the Coast. Springer Science, Berlin, pp 197–232

  • Lighthill MJ (1957) River Waves, Proceedings of 1st Symposium Naval Hydrodynamics, Washington, D. C. 1956, US National Research Council, 17–44

  • Liu PLF, Lynett P, Synolakis CE (2003) Analytical solutions for forced long waves on a sloping beach. J Fluid Mech 478:101–109

    Article  Google Scholar 

  • Madsen PA, Bingham HB, Liu H (2002) A new Boussinesq method for fully nonlinear waves from shallow to deep water. J Fluid Mech 462:1–30

    Article  Google Scholar 

  • Madsen PA, Bingham HB, Schaffer HA (2003) Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: derivation and analysis. Proc R Soc A 459:1075–1104

    Article  Google Scholar 

  • Madsen PA, Fuhrman DR (2007) Analytical and numerical models for tsunami run-up, tsunami and nonlinear waves. Springer, New York, pp 209–235

    Google Scholar 

  • Madsen PA, Fuhrman DR, Wang B (2006) A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast Eng 53:487–504

    Article  Google Scholar 

  • Mei CC, Kadri U (2018) Sound signals of tsunamis from a slender fault. J Fluid Mech 836:352–373

    Article  Google Scholar 

  • Menahem AB, Rosenman M (1972) Amplitude patterns of tsunami waves from submarine earthquakes. J Geophys Res 77:3097–3128

    Article  Google Scholar 

  • Mercer D et al (2002) Barotropic waves generated by storms moving rapidly over shallow water. J Geophys Res 107(C10):3152

    Article  Google Scholar 

  • Murotani S, Iwai M, Satake K, Shevchenko G, Loskutov A (2014) Tsunami forerunner of the 2011 tohoku earthquake observed in the sea of japan. Pure Appl Geophys 172:683–697

    Article  Google Scholar 

  • Murty TS (1978) Seismic sea Waves Tsunamis. Unipub, Canada, p 169

    Google Scholar 

  • Murty TS, Rao AD, Nirupama N, Nistor I (2006) Numerical modelling concepts for tsunami warning systems. Curr Sci 90(8):1073–1081

    Google Scholar 

  • Nosov M (1999) Tsunami generation in compressible ocean. Phys Chem Earth B 24(5):437–441

    Article  Google Scholar 

  • Nosov M, Kolesov S, Nurislamova G, Bolshakova A, Karpov V (2019) Effects of the Earth’s rotation on the dynamics of tsunami-like waves caused by deep-focus earthquakes. Geophys Res Abst 21:EGU2019–8514

    Google Scholar 

  • Okada Y (1985) Surface deformation due to shear and tensile fault in a half-space. Bull Seismologic Soc Amer 75(4):1135–1154

    Article  Google Scholar 

  • Okal EA, Synolakis CE (2016) Sequencing of tsunami waves: Why the first wave is not always the largest. Geophys J Int 204:719–735

    Article  Google Scholar 

  • Paris R (2015) Source mechanisms of volcanic tsunamis. Phil Trans R Soc A 373:1–15

    Article  Google Scholar 

  • Pattiaratchi CB, Wijeratne EMS (2015) Are meteotsunamis an underrated hazard? Phil Trans R Soc A 373:20140377

    Article  Google Scholar 

  • Rabinovich AB, Thomson RE, Stephenson FE (2006) The Sumatra tsunami of 26 December 2004 as observed in the North Pacific and North Atlantic oceans. Surv Geophys 27:647–677

    Article  Google Scholar 

  • Renzi E, Sammaraco P (2010) Landslide tsunamis propagating around a conical island. J Fluid Mech 650:251–285

    Article  Google Scholar 

  • Sammaraco P, Renzi E (2008) Landslide tsunamis propagating along a plane beach. J Fluid Mech 598:107–119

    Article  Google Scholar 

  • Stein S, Okal EA (2005) Speed and size of the Sumatra earthquake. Nature 434:581–582

    Article  Google Scholar 

  • Stiassnie M (2010) Tsunamis and acoustic–gravity waves from underwater earthquakes. J Eng Maths 67:23–32

    Article  Google Scholar 

  • Stoker JJ (1957) Water waves, 291. Interscience Publishers, New York

    Google Scholar 

  • Suppasri A, Imamura F, Koshimura S (2012) Tsunamigenic Ratio of the Pacific Ocean earthquakes and a proposal for a Tsunami Index. Nat Hazards Earth Syst Sci 12:175–185

    Article  Google Scholar 

  • Suppasri A, Shuto N, Imamura F, Koshimura S, Mas E, Yalciner AC (2013) Lessons learned from the 2011 Great East Japan tsunami: Performance of Tsunami Countermeasures, Coastal Buildings, and Tsunami Evacuation in Japan, Pure Appl. Geophys 170:993–1018

    Google Scholar 

  • Synolakis CE (1986) The runup of long waves, PhD thesis California Institute of Technology

  • Synolakis CE (1987) The runup of solitary waves. J Fluid Mech 185:523–545

    Article  Google Scholar 

  • Synolakis CE (1991) Tsunami Runup on Steep slopes: How Good Linear Theory Really is. Nat Hazards 4:221–234

    Article  Google Scholar 

  • Synolakis CE, Bardet JP, Borrero JC, Davies HL, Okal EA, Silver EA, Sweet S, Tappin DR (2002) The slump origin of the 1998 Papua New Guinea Tsunami. Proc R Soc Lond A 458:763–789

    Article  Google Scholar 

  • Synolakis CE, Bernard EN (2006) Tsunami science before and beyond Boxing Day 2004. Phil Trans R Soc A 364:2231–2265

    Article  Google Scholar 

  • Synolakis CE, Bernard EN, Titov VV, Kanoglu U, Gonzalez FI (2008) Validation and verification of tsunami numerical models. Pure Appl Geophys 165:2197–2228

    Article  Google Scholar 

  • Synolakis CE, Kanoglu U (2009) Development of benchmarked models. In: Bernard EN, Robinson AR (eds) The Sea 15. Harvard University Press, Cambridge

  • Synolakis CE, Kanoglu U (2015) The Fukushima accident was preventable. Phil Trans R Soc A 373:20140379

    Article  Google Scholar 

  • Talling PJ, Clare M, Urlaub M, Pope E, Hunt JE, Watt SFL (2014) Large submarine landslides on continental slopes: Geohazards, methane release, and climate change. Oceanography 27(2):32–45

    Article  Google Scholar 

  • Tappin DR, Watts P, Grilli ST (2008) The Papua New Guinea tsunami of 17 July 1998: Anatomy of a catastrophic event. Nat Hazards Earth Syst Sci 8:243–266

    Article  Google Scholar 

  • Tedapalli S, Synolakis CE (1994) The runup of N-Waves on sloping beach. Proc R Soc Lond A 445:99–112

    Article  Google Scholar 

  • Thorne L et al (2005) The Great Sumatra-Andaman Earthquake of 26 Dec 2004. Science 308:1127–1133

    Article  Google Scholar 

  • Tinti S, Tonini R (2005) Analytical evolution of tsunamis induced by near-shore earthquakes on a constant-slope ocean. J Fluid Mech 535:33–64

    Article  Google Scholar 

  • Titov VV, Moore C, Greenslade DJM, Pattiaratchi CB, Badal R, Synolakis CE (2011) A new tool for inundation mapping: community modeling interface for tsunamis (ComMIT). Pure Appl Geophys 168:2121–2131

    Article  Google Scholar 

  • Todorovska MI, Trifunac MD (2001) Generation of tsunamis by a slowly spreading uplift of the sea floor. Soil Dyn Earthq Eng 21:151–167

    Article  Google Scholar 

  • Trifunac MD, Todorovska MI (2002) A note on differences in tsunami source parameters for submarine slides and earthquakes. Soil Dynam Earthquake Eng 22:143–155

    Article  Google Scholar 

  • Trulsen K, Zeng H, Gramstad O (2012) Laboratory evidence of freak waves provoked by non-uniform bathymetry. Phys Fluids 24:097101–1-10

    Article  Google Scholar 

  • Tuck EO, Hwang LS (1972) Long wave generation on a sloping beach. J Fluid Mech 51 (3):449–461

    Article  Google Scholar 

  • Walker KT, Ishii M, Shearer PM (2005) Rupture details of the 28 March 2005 Sumatra Mw 8.6 earthquake imaged with teleseismic P waves. Geophys Res Lett 32:L24303

    Article  Google Scholar 

  • Ward SN, Asphaug E (2000) Asteroid impact tsunami: a probabilistic hazard assessment. Icarus 145:64–78

    Article  Google Scholar 

  • Wiegel RL (1955) Laboratory studies of gravity waves generated by the movement of a submerged body, Transactions. Amer Geophys Union 36(5):759–774

    Article  Google Scholar 

  • Wunnemann K, Weiss R (2015) The meteorite impact-induced tsunami hazard. Phil Trans R Soc A 373:1–14

    Article  Google Scholar 

  • Zahibo N, Pelinovsky E, Golinko V, Osipenko N (2006) Tsunami wave runup on coasts of narrow bays. Int J Fluid Mechan Res 33:106–118

    Article  Google Scholar 

Download references

Acknowledgements

The authors are deeply indebted to Prof. (Retd.) Asim Ranjan Sen, Department of Mathematics, Jadavpur University, India, for his help and suggestion during the preparation of this paper. Also comments from reviewers and the editor led to improvements in this manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arghya Bandyopadhyay.

Additional information

Responsible Editor: Richard John Greatbatch

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bandyopadhyay, A., Manna, S. & Maji, D. Hydrodynamic aspects of tsunami wave motion: a review. Ocean Dynamics 71, 613–629 (2021). https://doi.org/10.1007/s10236-021-01454-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10236-021-01454-z

Keywords

Navigation