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Landslides

pp 1–17 | Cite as

Simulation of energy transfers in waves generated by granular slides

  • Lucie ClousEmail author
  • Stéphane Abadie
Original Paper

Abstract

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.

Keywords

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

Nomenclature

η

Fluid dynamic viscosity [ML−1T−1]

μ

Friction coefficient

I

Inertial number

p

Fluid pressure [ML−1T−2]

D2

Second invariant of the strain rate tensor

μs, Δμ, I0

Material-dependent coefficients

d

Grain diameter [L]

ρ

Density [ML−3]

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

Fluid velocity [LT−1]

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

Gravitational acceleration [LT−2]

t

Time [T]

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

Viscous stress tensor [ML−1T−2]

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

Strain rate tensor [T−1]

t*

Relative time

h

Water depth [L]

Ep

Potential energy [ML2T−2]

Ek

Kinetic energy [ML2T−2]

Em

Mechanical energy [ML2T−2]

E0

Initial slide potential energy [ML2T−2]

Et

Transferred energy [ML2T−2]

Φ

Rate of the viscous dissipation [ML2T−3]

ϕ

Colour function

Δx

Horizontal length interval [L]

Δy

Vertical length interval [L]

λ

Energy transfer ratio

x

Horizontal coordinate [L]

y

Vertical coordinate [L]

Notes

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.

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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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