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Simulation of energy transfers in waves generated by granular slides

  • Lucie ClousEmail author
  • Stéphane Abadie
Original Paper


This paper presents a multi-fluid Navier-Stokes modeling of the waves generated by two granular slides (subaerial and submarine) which were previously studied experimentally and a pure synthetic submarine case used for results interpretation. In the numerical model, air and water are considered Newtonian fluids. The slide is modeled as a Newtonian fluid whose viscosity is adjusted to fit the experimental results. Once the viscosity is adjusted, the first and the second waves are shown to be accurately reproduced by the model even though the computed slide is slower. For the subaerial case, the viscosity value found is shown to be consistent with the granular μ(I) rheological law. The second part of this work focuses on the energy transfers between a slide and its generated waves. Energy balance is computed in each phase. The wave energy is evaluated in the wave propagation zone. Energy dissipation, kinematic and potential energies are taken into account in the computation of energy transfer ratio allowing for a better understanding of the phenomena. In light of these results, the wave train generation process is discussed as well as the importance of the slide dynamics in the wave generation stage. The amount of energy transferred to wave is not constant with time and the transfer rate depends strongly on the definition of this rate as well as the case considered. For instance, in the subaerial case simulated, the energy transferred to surface waves is 30% of the energy transferred to water at the time the transfer stops, but this conversion rate is only equal to 4% of the overall available potential slide energy at the end of the process. For the two submarine cases simulated, the corresponding values, equal in both cases, are 2% and 1%, respectively. The simulation results also show that the slide energy is transferred to the water in a short period of time at the beginning whatever the case considered. This observation may be related to the initial nil slide velocity (subaerial case) and the relatively large slope values considered (both cases). Nevertheless, the results illustrate the importance of accurate simulation of the slide dynamics within the wave generation process.


Landslide-generated waves Numerical simulations Multiphase model Energy transfer Subaerial slide Submarine slide Granular rheology 



Fluid dynamic viscosity [ML−1T−1]


Friction coefficient


Inertial number


Fluid pressure [ML−1T−2]


Second invariant of the strain rate tensor

μs, Δμ, I0

Material-dependent coefficients


Grain diameter [L]


Density [ML−3]

\( \underset{\_}{V} \)

Fluid velocity [LT−1]

\( \underset{\_}{g} \)

Gravitational acceleration [LT−2]


Time [T]

\( \underset{\_}{\underset{\_}{\tau }} \)

Viscous stress tensor [ML−1T−2]

\( \underset{\_}{\underset{\_}{D}} \)

Strain rate tensor [T−1]


Relative time


Water depth [L]


Potential energy [ML2T−2]


Kinetic energy [ML2T−2]


Mechanical energy [ML2T−2]


Initial slide potential energy [ML2T−2]


Transferred energy [ML2T−2]


Rate of the viscous dissipation [ML2T−3]


Colour function


Horizontal length interval [L]


Vertical length interval [L]


Energy transfer ratio


Horizontal coordinate [L]


Vertical coordinate [L]


Funding information

This work was funded by the FP7 EU research program ASTARTE (Grant No.: 603839), the PIA RSNR French program TANDEM (Grant No.: ANR-11-RSNR-00023-01) and the ANR RAVEX (ANR-16-CE03-0002) project. Financial support from the French Ministry of Higher Education, Research and Innovation for the PhD fellowship of Lucie Clous is gratefully acknowledged.


  1. Abadie S, Morichon D, Grilli S, Glockner S (2010) Numerical simulation of waves generated by landslides using a multiple-fluid Navier–stokes model. Coast Eng 57(9):779–794. CrossRefGoogle Scholar
  2. Abadie SM, Harris JC, Grilli ST, Fabre R (2012) Numerical modeling of tsunami waves generated by the flank collapse of the Cumbre Vieja Volcano (La Palma, Canary Islands): tsunami source and near field effects. J Geophys Res 117(C5).
  3. Ataie-Ashtiani B, Najafi-Jilani A (2008) Laboratory investigations on impulsive waves caused by underwater landslide. Coast Eng 55(12):989–1004CrossRefGoogle Scholar
  4. Ataie-Ashtiani B, Nik-Khah A (2008) Impulsive waves caused by subaerial landslides. Environ Fluid Mech 8(3):263–280. CrossRefGoogle Scholar
  5. Cassar C, Nicolas M, Pouliquen O (2005) Submarine granular flows down inclined planes. Phys Fluids 17(10):103,301. CrossRefGoogle Scholar
  6. Chassaing P (2000) Mécanique des fluides. Eléments d'un premier parcours Cépaduès éditionsGoogle Scholar
  7. Courant R, Friedrichs K, Lewy H (1967) On the partial difference equations of mathematical physics. IBM J Res Dev 11(2):215–234CrossRefGoogle Scholar
  8. Desombre J, Morichon D, Mory M (2012) Simultaneous surface and subsurface air and water flows modelling in the swash zone. Coast Eng Proc 1(33):56CrossRefGoogle Scholar
  9. Ducassou B, Nuñez J, Cruchaga M, Abadie S (2017) A fictitious domain approach based on a viscosity penalty method to simulate wave/structure interaction. J Hydraul Res 55(6):847–862CrossRefGoogle Scholar
  10. Fritz HM, Hager WH, Minor HE (2004) Near field characteristics of landslide generated impulse waves. J Waterw Port Coast Ocean Eng 130(6):287–302. CrossRefGoogle Scholar
  11. GDR MiDi (2004) On dense granular flows. Eur Phys J E 14(4):341–365. CrossRefGoogle Scholar
  12. Goda K (1979) A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows. J Comput Phys 30(1):76–95. CrossRefGoogle Scholar
  13. Grilli ST, Shelby M, Kimmoun O, Dupont G, Nicolsky D, Ma G, Kirby JT, Shi F (2017) Modeling coastal tsunami hazard from submarine mass failures: effect of slide rheology, experimental validation, and case studies off the US East Coast. Nat Hazards 86(1):353–391CrossRefGoogle Scholar
  14. Heinrich P (1992) Nonlinear water waves generated by submarine and aerial landslides. J Waterw Port Coast Ocean Eng 118(3):249–266CrossRefGoogle Scholar
  15. Heller V, Hager WH (2010) Impulse product parameter in landslide generated impulse waves. J Waterw Port Coast Ocean Eng 136(3):145–155. CrossRefGoogle Scholar
  16. Heller V, Hager W (2011) Wave types of landslide generated impulse waves. Ocean Eng 38(4):630–640CrossRefGoogle Scholar
  17. Heller V, Bruggemann M, Spinneken J, Rogers BD (2016) Composite modelling of subaerial landslide–tsunamis in different water body geometries and novel insight into slide and wave kinematics. Coast Eng 109:20–41CrossRefGoogle Scholar
  18. Ionescu IR, Mangeney A, Bouchut F, Roche O (2015) Viscoplastic modeling of granular column collapse with pressure-dependent rheology. J Non-Newtonian Fluid Mech 219:1–18. CrossRefGoogle Scholar
  19. Jiang L, LeBlond PH (1992) The coupling of a submarine slide and the surface waves which it generates. J Geophys Res 97(C8):12,731. CrossRefGoogle Scholar
  20. Jiang L, LeBlond PH (1993) Numerical modeling of an underwater Bingham plastic mudslide and the waves which it generates. J Geophys Res Oceans 98(C6):10,303–10,317CrossRefGoogle Scholar
  21. Kelfoun K, Giachetti T, Labazuy P (2010) Landslide-generated tsunamis at Réunion Island. J Geophys Res Earth Surf 115(F4)Google Scholar
  22. Lagrée PY, Staron L, Popinet S (2011) The granular column collapse as a continuum: validity of a two-dimensional Navier–Stokes model with a μ(I)-rheology. J Fluid Mech 686:378–408CrossRefGoogle Scholar
  23. Liu PF, Wu TR, Raichlen F, Synolakis C, Borrero J (2005) Runup and rundown generated by three-dimensional sliding masses. J Fluid Mech 536:107–144CrossRefGoogle Scholar
  24. Lo HY, Liu PLF (2017) On the analytical solutions for water waves generated by a prescribed landslide. J Fluid Mech 821:85–116. CrossRefGoogle Scholar
  25. Lynett P, Liu PLF (2002) A numerical study of submarine-landslide-generated waves and run-up. Proc R Soc A Math Phys Eng Sci 458(2028):2885–2910. CrossRefGoogle Scholar
  26. Ma G, Kirby JT, Hsu TJ, Shi F (2015) A two-layer granular landslide model for tsunami wave generation: theory and computation. Ocean Model 93:40–55CrossRefGoogle Scholar
  27. Mangeney-Castelnau A, Vilotte JP, Bristeau MO, Perthame B, Bouchut F, Simeoni C, Yerneni S (2003) Numerical modeling of avalanches based on Saint Venant equations using a kinetic scheme. J Geophys Res Solid Earth 108(B11)Google Scholar
  28. Mulligan RP, Take WA (2017) On the transfer of momentum from a granular landslide to a water wave. Coast Eng 125:16–22. CrossRefGoogle Scholar
  29. Pelinovsky E, Poplavsky A (1996) Simplified model of tsunami generation by submarine landslides. Phys Chem Earth 21(1–2):13–17CrossRefGoogle Scholar
  30. Pouliquen O, Forterre Y (2002) Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane. J Fluid Mech 453.
  31. Ruff LJ (2003) Some aspects of energy balance and tsunami generation by earthquakes and landslides. Pure Appl Geophys 160(10–11):2155–2176. CrossRefGoogle Scholar
  32. Sue LP, Nokes RI, Davidson MJ (2011) Tsunami generation by submarine landslides: comparison of physical and numerical models. Environ Fluid Mech 11(2):133–165. CrossRefGoogle Scholar
  33. Viroulet S (2013) Simulations de tsunamis générés par glissements de terrains aériens. Thèse de doctorat, Aix-Marseille Université, FranceGoogle Scholar
  34. Viroulet S, Sauret A, Kimmoun O, Kharif C (2013) Granular collapse into water: toward tsunami landslides. J Vis 16(3):189–191CrossRefGoogle Scholar
  35. Viroulet S, Sauret A, Kimmoun O (2014) Tsunami generated by a granular collapse down a rough inclined plane. EPL (Europhysics Letters) 105(3):34,004CrossRefGoogle Scholar
  36. Watts P (1997) Water waves generated by underwater landslides. PhD thesis, California Institute of technologyGoogle Scholar
  37. Watts P (1998) Wavemaker curves for tsunamis generated by underwater landslides. J Waterw Port Coast Ocean Eng 124(3):127–137CrossRefGoogle Scholar
  38. Watts P, 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):391–402. CrossRefGoogle Scholar
  39. Yavari-Ramshe S, Ataie-Ashtiani B (2017) A rigorous finite volume model to simulate subaerial and submarine landslide-generated waves. Landslides 14(1):203–221CrossRefGoogle Scholar
  40. Yavari-Ramshe S, Ataie-Ashtiani B (2019) On the effects of landslide deformability and initial submergence on landslide-generated waves. Landslides 16(1):37–53CrossRefGoogle Scholar
  41. Zhao T, Utili S, Crosta GB (2016) Rockslide and impulse wave modelling in the Vajont reservoir by DEM-CFD analyses. Rock Mech Rock Eng 49(6):2437–2456. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratoire des Sciences de l’Ingénieur Appliquées à la Mécanique et au génie Electrique, EA4581Université de Pau et des Pays de l’Adour, E2S UPPAAngletFrance

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