Skip to main content
SpringerLink
Log in

On numerical modelling of impulse water waves generated by submarine landslides

  • Thematic Issue
  • Published:
Environmental Earth Sciences Aims and scope Submit manuscript

Abstract

An algorithm is presented for numerical modelling of impulse water waves generated by submarine landslides moving along irregular bottom profiles. A spatially nonuniform submarine landslide moving on a spatially nonuniform slope is modelled by a “quasi-deformed” rigid body. In addition, a simplified model is studied for the particular case of landslide and bottom profiles dependent on one spatial coordinate only. Both models are used for the comparative analysis of numerical and experimental data for submarine rigid landslides moving along a plane slope. The simplified model is applied to analyse the dependences of wave characteristics on various parameters for submarine landslides moving along a sea bottom slope with monotonically increasing depth and in a bounded reservoir. The full model is used to study the landslide trajectories and the wave patterns for the model submarine landslide of a spatially irregular shape moving in the model reservoir with a spatially irregular bottom. All numerical computations are performed using the nonlinear shallow water equations with moving bottom and the time-stepping algorithm provided by a predictor–corrector scheme on adaptive grids.

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

Access this article

Log in via an institution

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
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Beisel SA, Chubarov LB, Khakimzyanov GS (2011) Simulation of surface waves generated by an underwater landslide moving over an uneven slope. Russ J Numer Anal Math Modell 26(1):17

    Google Scholar 

  • Beisel SA, Khakimzyanov GS, Khudyakova VK, Chubarov LB, Shokina NY (2011) Numerical modelling of surface waves generated by underwater landslides in reservoirs. Proc Razzakov Kyrgyz State Tech Univ (in Russian) 24:146

    Google Scholar 

  • Beisel SA, Chubarov LB, Dutykh D, Khakimzyanov GS, Shokina NY (2012) Simulation of surface waves generated by an underwater landslide in a bounded reservoir. Russ J Numer Anal Math Modell 27(6):539

    Google Scholar 

  • Buchgolz NN (1972) Basic course on theoretical mechanics. Part 1 (in Russian). Nauka, Moscow

  • Chubarov LB, Khakimzyanov GS, Shokina N (2011) Computational science and high performance computing IV. In: Krause E, Shokin Y, Resch M, Kröner D, Shokina N (eds) Notes on numerical fluid mechanics and multidisciplinary design, vol 115. Springer, New York, pp 75–91. doi:10.1007/978-3-319-00972-8

  • Chubarov LB, Eletskii SV, Fedotova ZI, Khakimzyanov GS (2005) Simulation of surface waves generation by an underwater landslide. Russ J Numer Anal Math Modell 20(5):425

    Article  Google Scholar 

  • Eletskii SV, Maiorov YB, Maksimov VV, Nudner IS, Fedotova ZI, Khazhoyan MG, Khakimzyanov GS, Chubarov LB (2004) Simulation of surface waves generation by a moving part of the bottom down the coastal slope. Computational technologies (in Russian), Special issue, part 2, p 194

  • Enet F, Grilli ST (2007) Experimental study of tsunami generation by three-dimensional rigid underwater landslides. J Waterw Port Coastal Ocean Eng 133(6):442

    Article  Google Scholar 

  • Fedotova ZI, Chubarov LB, Shokin YI (2004) Modelling of surface waves generated by landslides. Comput Technol (in Russian) 9(6):89

    Google Scholar 

  • Fedotova ZI, Khakimzyanov GS, Dutykh D (2014) On the energy equation of approximate models in the long-wave hydrodynamics. Russ J Numer Anal Math Modell 29(3):167

    Google Scholar 

  • Grilli ST, Watts P (2005) Tsunami generation by submarine mass failure. I: Modeling, experimental validation, and sensitivity analyses. J Waterw Port Coast Ocean Eng 131(6):283

    Article  Google Scholar 

  • Grilli ST, Watts P (1999) Modeling of waves generated by a moving submerged body. Applications to underwater landslides. Eng Anal Boundary Elem 23:645

    Article  Google Scholar 

  • Gusiakov VK (2009) Tsunami history - recorded. Sea Tsunamis 15:23

    Google Scholar 

  • Harahap ISH, Huan VNP (2014) Generation, propagation, run-up and impact of landslide triggered tsunami: a literature review. Appl Mech Mater 567:724. doi:10.4028/www.scientific.net/AMM.567.724

    Article  Google Scholar 

  • Harbitz CB, Pedersen G, Gjevik B (1993) Numerical simulation of large water waves due to landslides. J Hydraul Eng 119:1325

    Article  Google Scholar 

  • Heidarzadeh M, Krastel S, Yalciner AC (2014) Submarine mass movements and their consequences. In: Krastel S, Behrmann JH, Völker D, Stipp M, Berndt C, Urgeles R, Chaytor J, Huhn K, Strasser M, Harbitz CB (eds) Advances in natural and technological hazards research, vol 37. Springer, New York, pp 483–495. doi:10.1007/978-3-319-00972-8

  • Heller V, Hager WH, Minor HE (2009) Mitteilungen der Versuchsanstalt fur Wasserbau, Hydrologie und Glaziologie an der Eidgenossischen Technischen Hochschule Zurich, vol 211, p 1

  • Heller V, Hager W (2014) A universal parameter to predict subaerial landslide tsunamis? J Mar Sci Eng 2(2):400

    Article  Google Scholar 

  • Heller V, Spinneken J (2013) Improved landslide-tsunami prediction: effects of block model parameters and slide model. J Geophys Res Ocean 118(3):1489. doi:10.1002/jgrc.20099

    Article  Google Scholar 

  • Khakimzyanov GS, Shokina NY (2010) Numerical modelling of surface water waves generated by moving underwater landslide on irregular bottom. Comput Technol (in Russian) 15(1):105

    Google Scholar 

  • Khakimzyanov GS, Shokina NY (2012) Evaluation of the height of waves generated by an underwater landslide in a confined water reservoir. J Appl Mech Tech Phys 53(5):690

    Article  Google Scholar 

  • Khakimzyanov GS, Shokina NY (2012) Some notes on monotonicity preserving schemes. Comput Technol (in Russian) 17(2):79

    Google Scholar 

  • Khakimzyanov GS, Shokina NY (2013) Adaptive grid method for one-dimensional shallow water equations. Comput Technol (in Russian) 18(3):54

    Google Scholar 

  • Ma G, Kirby JT, Shi F (2013) Numerical simulation of tsunami waves generated by deformable submarine landslides. Ocean Model 69:146. doi:10.1016/j.ocemod.2013.07.001

    Article  Google Scholar 

  • Ostapenko VV (1999) Numerical simulation of wave flows caused by a shoreside landslide. J Appl Mech Tech Phys 40(4):647

    Article  Google Scholar 

  • Pelinovsky E, Poplavsky A (1996) Simplified model of tsunami generation by submarine landslides. Phys Chem Earth 21(12):13

    Article  Google Scholar 

  • Risio MD, Bellotti G, Panizzo A, Girolamo PD (2009) Three-dimensional experiments on landslide generated waves at a sloping coast. Coast Eng 56(5–6):659

    Article  Google Scholar 

  • Shokin YI, Fedotova ZI, Khakimzyanov GS, Chubarov LB, Beisel SA (2007) Modelling surfaces waves of generated by a moving landslide with allowance for vertical flow structure. Russ J Numer Anal Math Modell 22(1):63

    Google Scholar 

  • Shokin YI, Beisel SA, Gusev OI, Khakimzyanov GS, Chubarov LB, Shokina NY (2014) Numerical investigation of dispersive waves generated by landslide motion. Bull South Ural State Univ (in Russian) 7(1):121

    Google Scholar 

  • Shokina NY (2012) To the problem of construction of difference schemes on movable grids. Russ J Numer Anal Math Modell 27(6):603

    Google Scholar 

  • Watts P, Imamura F, Grilli ST (2000) Comparing model simulations of three benchmark tsunami generation cases. Sci Tsunami Hazards 18(2):107

    Google Scholar 

  • Watts P, Imamura F, Grilli ST, Kirby JT, Fryer GJ, Tappin DR (2003) Landslide tsunami case studies using a Boussinesq model and a fully nonlinear tsunami generation model. Nat Hazards Earth Syst Sci 3(5):391

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rechenzentrum, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 10, 79104, Freiburg im Breisgau, Germany

    Nina Shokina

  2. Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Vadym Aizinger

Authors
  1. Nina Shokina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vadym Aizinger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nina Shokina.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shokina, N., Aizinger, V. On numerical modelling of impulse water waves generated by submarine landslides. Environ Earth Sci 74, 7387–7405 (2015). https://doi.org/10.1007/s12665-015-4746-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12665-015-4746-3

Keywords

Mathematics Subject Classification

Search

Navigation