To improve our current understanding of tsunami-like solitary waves interacting with sandy beach, a nonlinear three-dimensional numerical model based on the computational fluid dynamics (CFD) tool OpenFOAM® is first self-developed to better describe the wave propagation, sediment transport, and the morphological responses of seabed during wave runup and drawdown. The finite volume method (FVM) is employed to discretize the governing equations of Navier–Stokes equations, combining with an improved volume of fluid (VOF) method to track the free surface and a k–ε model to resolve the turbulence. The computational capability of the hydrodynamics and the sediment transport module is well calibrated by laboratory data from different published references. The results verify that the present numerical model can satisfactorily reproduce the flow characteristics, and sediment transport processes under a tsunami-like solitary wave. The water-sediment transport module is then applied to investigate the effects of prominent factors, such as wave height, water depth, and beach slope, in affecting the beach profile change. Finally, a dimensionless empirical equation is proposed to describe the transport volume of onshore sediment based on simulation results, and some proper parameters are recommended through the regression. The results can be significantly helpful to evaluate the process of transported sediment by a tsunami event.

References

References
1.
Titov
,
V.
,
Rabinovich
,
A. B.
,
Mofjeld
,
H. O.
,
Thomson
,
R. E.
, and
González
,
F. I.
,
2005
, “
The Global Reach of the 26 December 2004 Sumatra Tsunami
,”
Science
,
309
(
5743
), pp.
2045
2048
.
2.
Mori
,
N.
, and
Takahashi
,
T.
,
2012
, “
Nationwide Post Event Survey and Analysis of the 2011 Tohoku Earthquake Tsunami
,”
Coastal Eng. J.
,
54
(
1
), pp.
1
27
.
3.
Morton
,
R. A.
,
Gelfenbaum
,
G.
, and
Jaffe
,
B. E.
,
2007
, “
Physical Criteria for Distinguishing Sandy Tsunami and Storm Deposits Using Modern Examples
,”
Sediment. Geol.
,
200
(
3
), pp.
184
207
.
4.
Jaffe
,
B. E.
,
Goto
,
K.
,
Sugawara
,
D.
,
Richmond
,
B.
,
Fujino
,
S.
, and
Nishimura
,
Y.
,
2012
, “
Flow Speed Estimated by Inverse Modeling of Sandy Tsunami Deposits: Results From the 11 March 2011 Tsunami on the Coastal Plain Near the Sendai Airport, Honshu, Japan
,”
Sediment. Geol.
,
282
, pp.
90
109
.
5.
Jaffe
,
B.
,
Gelfenbaum
,
G.
,
Rubin
,
D.
,
Peters
,
R.
,
Anima
,
R.
,
Swensson
,
M.
,
Olceses
,
D.
,
Bernales
,
L.
,
Gomez
,
J.
, and
Riega
,
P.
,
2003
, “
Identification and Interpretation of Tsunami Deposits From the June 23, 2001 Perú Tsunami
,”
Proceedings of International Conference on Coastal Sediments
,
Orlando, FL
, pp.
1
13
.
6.
Paris
,
R.
,
Lavigne
,
F.
,
Wassmer
,
P.
, and
Sartohadi
,
J.
,
2007
, “
Coastal Sedimentation Associated With the December 26, 2004 Tsunami in Lhok Nga, West Banda Aceh (Sumatra, Indonesia)
,”
Mar. Geol.
,
238
(
1
), pp.
93
106
.
7.
Szczuciński
,
W.
,
Kokociński
,
M.
,
Rzeszewski
,
M.
,
Chagué-Goff
,
C.
,
Cachão
,
M.
,
Goto
,
K.
, and
Sugawara
,
D.
,
2012
, “
Sediment Sources and Sedimentation Processes of 2011 Tohoku-oki Tsunami Deposits on the Sendai Plain, Japan-Insights From Diatoms, Nannoliths and Grain Size Distribution
,”
Sediment. Geol.
,
282
(
1
), pp.
40
56
.
8.
Tzang
,
S. Y.
,
Chen
,
Y. L.
, and
Ou
,
S. H.
,
2011
, “
Experimental Investigations on Developments of Velocity Field Near Above a Sandy Bed During Regular Wave-Induced Fluidized Responses
,”
Ocean Eng.
,
38
(
7
), pp.
868
877
.
9.
Jiang
,
C.
,
Wu
,
Z.
,
Chen
,
J.
,
Deng
,
B.
,
Long
,
Y.
, and
Li
,
L.
,
2017
, “
An Available Formula of the Sandy Beach State Induced by Plunging Waves
,”
Acta Oceanol. Sin.
,
36
(
9
), pp.
91
100
.
10.
Kobayashi
,
N.
, and
Wurjanto
,
A.
,
1992
, “
Irregular Wave Setup and Run-Up on Beaches
,”
J. Waterway Port, Coastal, Ocean Eng.
,
118
(
4
), pp.
368
386
.
11.
Jacobsen
,
N. G.
, and
Fredsoe
,
J.
,
2014
, “
Formation and Development of a Breaker Bar Under Regular Waves. Part 2: Sediment Transport and Morphology
,”
Coastal Eng.
,
88
(
3
), pp.
55
68
.
12.
Dean
,
R. G.
,
1991
, “
Equilibrium Beach Profile: Characteristics and Application
,”
Coastal Res.
,
7
(
1
), pp.
53
84
.
13.
Larson
,
M.
,
Kraus
,
N. C.
, and
Wise
,
R. A.
,
1999
, “
Equilibrium Beach Profiles Under Breaking and Non-Breaking Waves
,”
Coastal Eng.
,
36
(
1
), pp.
59
85
.
14.
Sénéchal
,
N.
,
Dupuis
,
H.
,
Bonneton
,
P.
,
Howa
,
H.
, and
Pedreros
,
R.
,
2001
, “
Observation of Irregular Wave Transformation in the Surf Zone Over a Gently Sloping Sandy Beach on the French Atlantic Coastline
,”
Oceanol. Acta
,
24
(
6
), pp.
545
556
.
15.
Stark
,
N.
, “
Pore Pressure Response to Irregular Waves at a Sandy Beach
,”
Geotechnical Frontiers 2017
,
March 12–15, 2017
,
Orlando, FL
, pp.
409
417
.
16.
Lin
,
P.
,
2004
, “
A Numerical Study of Solitary Wave Interaction With Rectangular Obstacles
,”
Coastal Eng.
,
51
(
1
), pp.
35
51
.
17.
Kobayashi
,
N.
, and
Lawrence
,
A. R.
,
2004
, “
Cross-Shore Sediment Transport Under Breaking Solitary Waves
,”
J. Geophys. Res.
,
109
(
C3
), pp.
1
13
.
18.
Moronkeji
,
A.
, and
Rolla
,
O. H.
, “
Physical Modelling of Tsunami Induced Sediment Transport and Scour
,”
Proceedings of the 2007 Earthquake Engineering Symposium for Young Researchers
,
Seattle, WA
,
2007
, pp.
8
12
.
19.
Tsujimoto
,
G.
,
Kakinoki
,
T.
, and
Yamada
,
F.
,
2008
, “
Time-Space Variation and Spectral Evolution of Sandy Beach Profiles Under Tsunami and Regular Waves
,”
The Eighteenth International Offshore and Polar Engineering Conference, International Society of Offshore and Polar Engineers
,
Vancouver, Canada
, pp.
1
5
.
20.
Young
,
Y. L.
,
Xiao
,
H.
, and
Maddux
,
T.
,
2010
, “
Hydro- and Morpho-Dynamic Modeling of Breaking Solitary Waves Over a Fine Sand Beach. Part I: Experimental Study
,”
Mar. Geol.
,
269
(
3–4
), pp.
107
118
.
21.
Jiang
,
C.
,
Chen
,
J.
,
Yao
,
Y.
,
Liu
,
J.
, and
Deng
,
Y.
,
2015
, “
Study on Threshold Motion of Sediment and Bedload Transport by Tsunami Waves
,”
Ocean Eng.
,
100
(
1
), pp.
97
106
.
22.
Daghighi
,
N.
,
Chegini
,
A. H. N.
,
Daliri
,
M.
, and
Hedayati
,
D.
,
2015
, “
Experimental Assessment of Sediment Transport and Bed Formation of Sandy Beaches by Tsunami Waves
,”
Int. J. Environ. Res.
,
9
(
3
), pp.
795
804
.
23.
Simpson
,
G.
, and
Castelltort
,
S.
,
2006
, “
Coupled Model of Surface Water Flow, Sediment Transport and Morphological Evolution
,”
Comput. Geosci.
,
32
(
10
), pp.
1600
1614
.
24.
Pritchard
,
D.
, and
Dickinson
,
L.
,
2008
, “
Modelling the Sedimentary Signature of Long Waves on Coasts: Implications for Tsunami Reconstruction
,”
Sediment. Geol.
,
206
(
1
), pp.
42
57
.
25.
Shimozono
,
T.
,
Sato
,
S.
, and
Tajima
,
Y.
,
2007
, “
Numerical Study of Tsunami Run-Up Over Erodible Sand Dunes
,”
Sixth International Symposium on Coastal Engineering and Science of Coastal Sediment Process
,
New Orleans, LA
, pp.
1089
1102
.
26.
Xiao
,
H.
,
Young
,
Y. L.
, and
Prévost
,
J. H.
,
2010
, “
Hydro- and Morpho-Dynamic Modeling of Breaking Solitary Waves Over a Fine Sand Beach. Part II: Numerical Simulation
,”
Mar. Geol.
,
269
(
3
), pp.
119
131
.
27.
Nakamura
,
T.
, and
Yim
,
S. C.
,
2011
, “
A Nonlinear Three-Dimensional Coupled Fluid-Sediment Interaction Model for Large Seabed Deformation
,”
ASME J. Offshore Mech. Arct. Eng.
,
133
(
3
), p.
031103
.
28.
Jacobsen
,
N. G.
,
Fuhrman
,
D. R.
, and
Fredsøe
,
J.
,
2012
, “
A Wave Generation Toolbox for the Open-Source CFD Library: OpenFoam®
,”
Int. J. Numer. Methods Fluids
,
70
(
9
), pp.
1073
1088
.
29.
Higuera
,
P.
,
Lara
,
J. L.
, and
Losada
,
I. J.
,
2013
, “
Realistic Wave Generation and Active Wave Absorption for Navier–Stokes Models: Application to OpenFOAM®
,”
Coastal Eng.
,
71
(
1
), pp.
102
118
.
30.
Liang
,
D.
,
Cheng
,
L.
, and
Li
,
F.
,
2005
, “
Numerical Modeling of Flow and Scour Below a Pipeline in Currents: Part II. Scour Simulation
,”
Coastal Eng.
,
52
(
1
), pp.
43
62
.
31.
Jacobsen
,
N. G.
, and
Fredsøe
,
J.
,
2011
, “
A Full Hydro- and Morphodynamic Description of Breaker Bar Development
,” Ph.D. thesis,
Technical University of Denmark
,
Kongens Lyngby
.
32.
Jiang
,
C. B.
,
Liu
,
X. J.
,
Yao
,
Y.
,
Deng
,
B.
, and
Chen
,
J.
,
2017
, “
Numerical Investigation of Tsunami-Like Solitary Wave Interaction With a Seawall
,”
J. Earthq. Tsunami
,
11
(
1
), pp.
1
18
.
33.
Babaeyan-Koopaei
,
K.
,
Ervine
,
D. A.
,
Carling
,
P. A.
, and
Cao
,
Z.
,
2002
, “
Velocity and Turbulence Measurements for Two Overbank Flow Events in River Severn
,”
J. Hydraul. Eng.
,
128
(
10
), pp.
891
900
.
34.
Schlichting
,
H.
,
1979
,
Boundary-Layer Theory
,
McGraw-Hill Book Company
,
New York
.
35.
Zeng
,
J.
,
Constantinescu
,
G.
, and
Weber
,
L.
,
2005
, “
A Fully 3D Non-Hydrostatic Model for Prediction of Flow, Sediment Transport and Bed Morphology in Open Channels
,”
Proceedings of the 31st IAHR Congress
,
Seoul, South Korea
, pp.
1327
1338
.
36.
Galperin
,
B.
,
Kantha
,
L. H.
,
Hassid
,
S.
, and
Rosati
,
A.
,
1988
, “
A Quasi-Equilibrium Turbulent Energy Model for Geophysical Flows
,”
J. Atmos. Sci.
,
45
(
1
), pp.
55
62
.
37.
Arzani
,
A.
,
Gambaruto
,
A. M.
,
Chen
,
G.
, and
Shadden
,
S. C.
,
2016
, “
Lagrangian Wall Shear Stress Structures and Near-Wall Transport in High-Schmidt-Number Aneurysmal Flows
,”
J. Fluid Mech.
,
790
(
1
), pp.
158
172
.
38.
Smith
,
J. D.
, and
McLean
,
S. R.
,
1977
, “
Spatially Averaged Flow Over a Wavy Surface
,”
J. Geophys. Res.
,
82
(
12
), pp.
1735
1746
.
39.
Rijn
,
L. C. V.
,
1985
, “
Sediment Transport, Part I: Bed Load Transport
,”
J. Hydraul. Eng.
,
110
(
10
), pp.
1431
1456
.
40.
Soulsby
,
R. L.
, and
Whitehouse
,
R. J. S. W.
,
1997
, “
Threshold of Sediment Motion in Coastal Environments
,”
Pacific Coasts and Ports 1997 Conference
,
Christchurch, New Zealand
, pp.
149
154
.
41.
Engelund
,
F.
, and
Fredsøe
,
J.
,
1976
, “
A Sediment Transport Model for Straight Alluvial Channels
,”
Hydrol. Res.
,
7
(
5
), pp.
293
306
.
42.
Allen
,
J. R. L.
,
1982
, “
Simple Models for the Shape and Symmetry of Tidal Sand Waves: (1) Statically Stable Equilibrium Forms
,”
Mar. Geol.
,
48
(
1
), pp.
31
49
.
43.
Brørs
,
B.
,
1999
, “
Numerical Modeling of Flow and Scour at Pipelines
,”
J. Hydraul. Eng.
,
125
(
5
), pp.
511
523
.
44.
Liu
,
X.
, and
García
,
M. H.
,
2008
, “
Three-Dimensional Numerical Model With Free Water Surface and Mesh Deformation for Local Sediment Scour
,”
J. Waterway Port, Coastal, Ocean Eng.
,
134
(
4
), pp.
203
217
.
45.
Richardson
,
J. F.
, and
Zaki
,
W. N.
,
1997
, “
Sedimentation and Fluidisation: Part I
,”
Chem. Eng. Res. Des.
,
75
(
1
), pp.
82
100
.
46.
Leveque
,
R. J.
,
2007
,
Finite Volume Methods for Hyperbolic Problems
,
Cambridge University Press
,
Cambridge
.
47.
Rijn
,
L. C.
,
1984
, “
Sediment Transport, Part II: Suspended Load Transport
,”
J. Hydraul. Eng.
,
110
(
11
), pp.
1613
1641
.
48.
Jasak
,
H.
, and
Tukovic
,
Z.
,
2006
, “
Automatic Mesh Motion for the Unstructured Finite Volume Method
,”
Trans. FAMENA
,
30
(
2
), pp.
1
20
.
49.
Khosronejad
,
A.
,
Kang
,
S.
,
Borazjani
,
I.
, and
Sotiropoulos
,
F.
,
2011
, “
Curvilinear Immersed Boundary Method for Simulating Coupled Flow and Bed Morphodynamic Interactions Due to Sediment Transport Phenomena
,”
Adv. Water Resour.
,
34
(
7
), pp.
829
843
.
50.
Lee
,
J. J.
,
Skjelbreia
,
J. E.
, and
Raichlen
,
F.
,
1982
, “
Measurement of Velocities in Solitary Waves
,”
J. Waterway Port, Coastal, Ocean Div.
,
108
(
2
), pp.
200
218
.
51.
Rijn
,
L. C.
,
1986
, “
Mathematical Modeling of Suspended Sediment in Nonuniform Flows
,”
J. Hydraul. Eng.
,
112
(
6
), pp.
433
455
.
52.
Wu
,
W.
,
Rodi
,
W.
, and
Wenka
,
T.
,
2000
, “
3D Numerical Modeling of Flow and Sediment Transport in Open Channels
,”
J. Hydraul. Eng.
,
126
(
1
), pp.
4
15
.
53.
Willmott
,
C. J.
,
1981
, “
On the Validation of Models
,”
Phys. Geogr.
,
2
(
2
), pp.
184
194
.
54.
Synolakis
,
C. E.
,
1987
, “
The Runup of Solitary Waves
,”
J. Fluid Mech.
,
185
(
1
), pp.
523
545
.
55.
Dean
,
R. G.
, and
Dalrymple
,
R. A.
,
1991
, “
Water Wave Mechanics for Engineers and Scientists
,”
Advanced Series on Ocean Engineering 2
,
World Scientific
,
Farrer Road
.
56.
Jacobsen
,
N. G.
,
2015
, “
Mass Conservation in Computational Morphodynamics: Uniform Sediment and Infinite Availability
,”
Int. J. Numer. Methods Fluids
,
78
(
4
), pp.
233
256
.
You do not currently have access to this content.