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Numerical modeling of subaerial and submarine landslide-generated tsunami waves—recent advances and future challenges

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Abstract

Landslide-generated waves (LGWs) are among natural hazards that have stimulated attentions and concerns of engineers and researchers during the past decades. At the same period, the application of numerical modeling has been progressively increased to assess, control, and manage the risks of such hazards. This paper represents an overview of numerical studies on LGWs to explore associated recent advances and future challenges. In this review, the main landslide events followed by an LGW hazard are scrutinized. The uncertainty regarding landslide characteristics and the lack of data concerning generated tsunami properties highlights the necessity of probabilistic analysis and numerical modeling. More than 53 % of landslides show the slide length larger than about 20 times of the slide thickness. This fact justifies the popular application of depth-averaged equations (DAEs) for landslides’ motion simulations. Such models are reviewed and tabulated based on their mathematical, numerical, and conceptual approaches. A landslide is generally treated as a homogeneous, mixture, or a multi-phase fluid with different rheologies. The Coulomb type rheology is the most-used rheology applied in more than 70 % of landslide models. Some of the recent studies are considering the effects of multi-phase nature, dynamic changes of rheological parameters, and grain-size segregation of the landslide on its deformations. The numerical tools that model LGWs are also reviewed, categorized, and examined. These models conceptualize a landslide as a general rigid LGW (R-LGW) or deformable LGW (D-LGW) mass. The rigid slide assumption is mainly applied in the LGW models with a focus on the accurate simulation of the wave propagation stage, particularly by means of higher order Boussinesq-type wave equations (BWEs). The majority of D-LGW models solve either the Navier–Stokes equations (NSEs) for a multi-phase (landslide material, water, and air) flow or the shallow water equations (SWEs) for a two-layer (a layer of granular material moving beneath a layer of water) flow. NSEs are more comprehensive models but less robust than DAEs. The key effect of dispersion in LGWs, which are typically important in intermediate and even deep water wave domains, challenges researchers to apply higher order BWEs instead of SWEs in two-layer models. Regarding numerical approaches, Lagrangian’s are more robust than Eulerian’s, but they have been rarely applied due to their high computational demands for real cases. The remaining challenges are reviewed as the necessity of probabilistic analysis to assess the risk of the related hazards more accurately for both past and potential LGW hazards; further thorough laboratory-scale experiments and field data measurements to have accurate and detailed benchmark data; providing RS/GIS-based worldwide hazard map for potential LGWs and compiled database for occurred events; extending BWEs for granular flows and DAEs with non-hydrostatic corrections; and economizing the computational costs of models by advanced techniques like parallel processing and GPU accelerators.

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Abbreviations

1L:

One layer

2D:

Two-dimensional

2HD:

Two-dimensional in horizontal surface

3DEs:

Three-dimensional equations

ALE:

Arbitrary Lagrangian-Eulerian

ANOVA:

Analysis of variance

BC:

Boundary condition

BEM:

Boundary element method

BM:

Bermudez-Moreno

BTE:

Boussinesq type equation

BWEs:

Boussinesq water wave equations

CAMR:

Continuous adaptive mesh refinement

Const.:

Constant

C-NSE:

Compressible NSE

CP:

Cauchy-Poison

CPU:

Central processing unit

DA:

Depth averaged

DAE:

Depth-averaged equation

Deg:

Degree

DEM:

Discrete element method

DI:

Depth integrated

Dim:

Dimension

D-LGW:

Deformable-LGW

DR:

Deformable rigid

El:

Elliptical-shape

EQ M w :

Earthquake moment magnitude

EE:

Empirical equation

EGW:

Earthquake-generated wave

Eq.:

Equation

FDM:

Finite difference method

FEM:

Finite element method

FVM:

Finite volume method

G:

Gaussian-shaped

Gen.:

Generation

GIS:

Geographical information system

GLOFs:

Glacial lake outburst floods

Gov.:

Governing

GPU:

Graphics processing unit

GRASS:

Geographic resources analysis support system

H:

Hyperbolic-shaped

HLL:

Harten, Lax, and Van Leer

HLLC:

HLL contact

HPC:

High performance computing

Ini.:

Initiation

IPL:

The International Programme on Landslides

ITST:

International Tsunami Survey Team

JAMSTEC:

Japan Marine Science and Technology Center

Kg:

Kilogram

km :

Kilometer

Km3 :

Cubic kilometer

L:

Lagrangian

LS:

Level set

LGW:

Landslide-generated wave

LHLL:

Lateralized HLL

LM:

Lumped mass

m:

Meter

m3 :

Cubic meter

MAC:

Marker and cell

M FV-FE:

Mixed FVM-FEM

MM:

Mixture model

MOST:

Method of splitting tsunami model

MPM:

Multi-phase model

MPS:

Moving particle semi-implicit

MRB:

Moving rigid box

M w :

Moment magnitude

NGDC:

National Geophysical Data Center

NHM:

Non-hydrostatic model

NHWAVE:

Non-hydrostatic WAVE

NOAA:

National Oceanic and Atmospheric Administration

NOC:

Non-oscillatory central

NSEs:

Navier–Stokes equations

Num.:

Numerical

PFEs:

Potential flow equations

PNG:

Papua New Guinea

Prop.:

Propagation

PSFA:

Prandtl’s slender flow approximations

RAMMS:

Rapid mass movements model

RANS:

Reynolds-averaged NSEs

Re.:

Rectangular

R-LGW:

Rigid-LGW

RS:

Remote sensing

SAGE:

SAIC adaptive grid Eulerian code

SAL:

Subaerial landslide

SALGW:

Subaerial landslide-generated wave

SAMOS:

Snow avalanche modeling and simulation

SEM:

Surface elevation method

SML:

Submarine landslide

SMLGW:

Submarine landslide-generated wave

SOPAC:

South Pacific Applied Geoscience Commission

SPH:

Smoothed particle hydrodynamics

SPM:

Single phase model

SWEs:

Shallow water equations

THETIS:

A numerical model

THINC:

Tangent of hyperbola for interface capturing

TIME:

Tsunami inundation modeling exchange model

TUNAMI:

Tohoku University’s numerical analysis model for tsunamis

TVB:

Time variable bottom boundary

V:

Varying geometry

VOF:

Volume of fluid

WA:

Width averaged

WAF:

Weighted average flux method

WS-IC:

Water surface-initial condition

SPH:

Smoothed particle hydrodynamics

a :

Wave amplitude

a max :

Maximum wave amplitude

a nmax :

Maximum negative wave amplitude

a pmax :

Maximum positive wave amplitude

a′:

Constant factor

b :

Bottom topography b(x, y)

b′:

A function of f(u)

c z :

Chezy coefficient

c k :

Mass fraction of k-th phase of a mixture

d :

h + εζ

d 0 :

Particle diameter

f :

A function

F :

Force

h :

Water depth

h 0 :

Still water depth

h 0c :

Landslide initial depth due to water surface

h max :

Maximum wave height

h t :

∂h/∂t

I :

Inertial number \( I=\left|\dot{\gamma}\right|{d}_0/\sqrt{P/{\rho}_s} \)

k :

Number of landslide phases

K D :

Dilatant consistency index

K HB :

Herschel–Bulkley consistency index

l s :

Landslide length

n :

Constant

P :

Pressure

P S :

Water surface pressure BC

r :

Wave distance from landslide impact area

R :

Wave runup height

S :

Landslide thickness

t :

Time

u :

Wave velocity component in x direction

u′:

Landslide velocity in the bottom direction

U :

Velocity vector U(t) = (u(t), v(t), w(t))

\( \overset{-}{u} \) :

Depth-averaged u

v :

Wave velocity component in y direction

V :

Landslide volume

\( \overset{-}{v} \) :

Depth-averaged v

w :

Wave velocity component in z direction

u m :

Bulk velocity of a mixture

w s :

Landslide width

X :

Landslide distance travelled in a given time in x direction

Y :

Landslide distance travelled in a given time in y direction

z′:

Landslide velocity in the sliding slope direction

\( \overset{\sim }{z} \) :

A weighted-average characteristic variable depth

Z :

Time variable landslide location Z(x, y, t)

Z 0 :

The initial landslide geometry

Z α :

Characteristic water depth

α :

Order of accuracy regarding wave non-linearity

α k :

Volume fraction of k-th phase of a mixture

β :

Order of accuracy regarding wave dispersion

γ slide :

Landslide bulk density

\( \dot{\gamma} \) :

Shear rate

δ :

Basal friction angle

ε :

Wave non-linearity index ε = a/h 0

θ :

Slope angle

λ :

Wavelength

μ :

Wave dispersion index μ = h 0/λ

μ B :

Bingham fluid viscosity

μ d :

Dynamic viscosity

μ eff :

Effective friction coefficient

μ(I):

A rheological model

ξ :

Wave height due to water surface

ρ :

Density

ρ K :

Density of the k-th phase of a mixture

ρ m :

Bulk density of a mixture

σ′:

Normal stress

τ :

Shear stress

τ b :

Bottom shear stress

τ c :

Critical shear stress

τ s :

Flow surface shear stress

φ :

Internal friction angle

ψ 0 :

Landslide porosity

Ο:

Order of accuracy

∇:

Gradient vector

(x, y, z):

Cartesian coordinate

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Acknowledgments

Authors appreciate the continued support of Civil Engineering department of Sharif University of Technology, Iran, for this research topic during the past 10 years. The second author acknowledges the contributions of his former graduate students including Dr. A. Najafi-Jilani, Dr. G.R. Shobayri, Eng. A. Nik-Khah, Dr. L. Farhadi, Dr. S. Malek-Mohammadi, Dr. S. Mansour-Rezaei, and Dr. R. Jalali-Farahani who had worked on this research topic. The authors wish to thank the editor-in-chief Professor Sassa for his thoughtful comments and also two anonymous reviewers for their valuable comments, which helped to improve the final manuscript.

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  1. Department of Civil Engineering, Sharif University of Technology, PO Box 11155-9313, Tehran, Iran

    S. Yavari-Ramshe & B. Ataie-Ashtiani

  2. National Center for Groundwater Research and Training and School of the Environment, Flinders University, GPO Box 2100, Adelide, South Australia, 5001, Australia

    B. Ataie-Ashtiani

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Yavari-Ramshe, S., Ataie-Ashtiani, B. Numerical modeling of subaerial and submarine landslide-generated tsunami waves—recent advances and future challenges. Landslides 13, 1325–1368 (2016). https://doi.org/10.1007/s10346-016-0734-2

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