Abstract
Propagation and impact of two- and three-dimensional bores generated by breaking of a water reservoir is studies by use of three theoretical models. These include the Reynolds-averaged Navier–Stokes (RANS) equations, the level I Green-Naghdi (GN) equations, and the Saint-Venant (SV) equations. Two types of bore generations are considered, namely, (i) bore generated by dam-break, where the reservoir water depth is substantially larger than the downstream water depth, and (ii) bore generated by an initial mound of water, where the reservoir water depth is larger but comparable to the downstream water depth. Each of these conditions corresponds to different natural phenomena. This study shows that the relative water depth plays a significant role on the bore shape, stability, and impact. Particular attention is given to the bore pressure on horizontal and vertical surfaces. The effect of fluid viscosity is studied by use of different turbulence closure models. Both two- and three-dimensional computations are performed to study their effect on bore dynamics. Results of the theoretical models are compared with each other and with available laboratory experiments. Information is provided on bore kinematics and dynamics predicted by each of these models. Discussion is given on the assumptions made by each model and differences in their results. In summary, SV equations have substantially simplified the physics of the problem, while results of the GN equations compare well with the RANS equations, with incomparable computational cost. RANS equations provide further details about the physics of the problem.
References
1.
Chanson
, H.
, 2006
, “Tsunami Surges on Dry Coastal Plains: Application of Dam Break Wave Equations
,” Coastal Eng. J.
, 48
(4
), pp. 355
–370
. 10.1142/S05785634060014772.
Cross
, R. H.
, 1967
, “Tsunami Surge Forces
,” J. Waterways Harbors Div.
, 93
(4
), pp. 201
–231
.3.
Yeh
, H.
, 2006
, “Maximum Fluid Forces in the Tsunami Runup Zone
,” J. Waterway, Port, Coastal, Ocean Eng.
, 132
(6
), pp. 496
–500
. 10.1061/(ASCE)0733-950X(2006)132:6(496)4.
Kihara
, N.
, Niida
, Y.
, Takabatake
, D.
, Kaida
, H.
, Shibayama
, A.
, and Miyagawa
, Y.
, 2015
, “Large-scale Experiments on Tsunami-Induced Pressure on a Vertical Tide Wall
,” Coastal Eng.
, 99
, pp. 46
–63
. 10.1016/j.coastaleng.2015.02.0095.
Linton
, D.
, Gupta
, R.
, Cox
, D.
, van de Lindt
, J.
, Oshnack
, M. E.
, and Clauson
, M.
, 2012
, “Evaluation of Tsunami Loads on Wood-Frame Walls At Full Scale
,” J. Struct. Eng.
, 139
(8
), pp. 1318
–1325
. 10.1061/(ASCE)ST.1943-541X.00006446.
Mizutani
, S.
, and Imamura
, F.
, 2001
, “Dynamic Wave Force of Tsunamis Acting on a Structure
,” Proceedings of the International Tsunami Symposium
, Seattle, WA
, Aug. 7–10
, pp. 7
–28
.7.
Robertson
, I. N.
, Paczkowski
, K.
, Riggs
, H.
, and Mohamed
, A.
, 2011
, “Tsunami Bore Forces on Walls
,” ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering
, Rotterdam, The Netherlands
, June 9–14
, American Society of Mechanical Engineers
, pp. 395
–403
.8.
Robertson
, I. N.
, Carden
, L. P.
, and Chock
, G. Y.
, 2013
, “Case Study of Tsunami Bore Impact on RC Wall
,” ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering, American Society of Mechanical Engineers
, Nantes, France
, June 9–14
, American Society of Mechanical Engineers
, pp. V005T06A077
–V005T06A085
.9.
Santo
, J.
, and Robertson
, I. N.
, 2010
, “Lateral Loading on Vertical Structural Elements Due to a Tsunami Bore
,” University of Hawaii
, Honolulu
, Report No. UHM/CEE/10-02, pp. 107
–137
.10.
Rahman
, S.
, Akib
, S.
, Khan
, M.
, and Shirazi
, S.
, 2014
, “Experimental Study on Tsunami Risk Reduction on Coastal Building Fronted by Sea Wall
,” Sci. World J.
, 2014
, pp. 94
–101
. 10.1155/ 2014/72935711.
Thusyanthan
, N. I.
, and Gopal Madabhushi
, S. P.
, 2008
, “Tsunami Wave Loading on Coastal Houses: A Model Approach
,” P. I. Civil Eng-Civ. En.
, 161
(2
), pp. 77
–86
.12.
Wijatmiko
, I.
, and Murakami
, K.
, 2012
, “Hydrodynamics: Theory and Model,” BoD–Books on Demand
, J.
Zheng
, ed., Intech
, Rijeka, Croatia
, pp. 59
–78
.13.
Asakura
, R.
, 2000
, “An Experimental Study on Wave Force Acting on On-Shore Structures Due to Overflowing Tsunamis
,” Proceedings of Coastal Engineering, JSCE
, 47
, pp. 911
–915
.14.
Chinnarasri
, C.
, Thanasisathit
, N.
, Ruangrassamee
, A.
, Weesakul
, S.
, and Lukkunaprasit
, P.
, 2013
, “The Impact of Tsunami-Induced Bores on Buildings
,” P. I. Civil Eng-Mar. En.
, 166
(1
), pp. 14
–24
.15.
Fujima
, K.
, Achmad
, F.
, Shigihara
, Y.
, and Mizutani
, N.
, 2009
, “Estimation of Tsunami Force Acting on Rectangular Structures
,” J. Disaster Res.
, 4
(6
), pp. 404
–409
. 10.20965/jdr.2009.p040416.
Nouri
, Y.
, Nistor
, I.
, Palermo
, D.
, and Cornett
, A.
, 2010
, “Experimental Investigation of Tsunami Impact on Free Standing Structures
,” Coastal Eng. J.
, 52
(01
), pp. 43
–70
. 10.1142/S057856341000211717.
Palermo
, D.
, Nistor
, I.
, Al-Faesly
, T.
, and Cornett
, A.
, 2012
, “Impact of Tsunami Forces on Structures: The University of Ottawa Experience
,” Proceedings of the Fifth International Tsunami Symposium
, Ispra, Italy
, Sept. 3–5
, pp. 43
–70
.18.
Palermo
, D.
, Nistor
, I.
, Nouri
, Y.
, and Cornett
, A.
, 2009
, “Tsunami Loading of Near-Shoreline Structures: A Primer
,” Can. J. Civil Eng.
, 36
(11
), pp. 1804
–1815
. 10.1139/L09-10419.
Robertson
, I.
, Riggs
, H.
, and Mohamed
, A.
, 2008
, “Experimental Results of Tsunami Bore Forces on Structures
,” 27th International Conference on Offshore Mechanics and Arctic Engineering.
Estoril, Portugal
, June 15–20
, Vol. 135
, pp. 585
–601
.20.
Pilotti
, M.
, Maranzoni
, A.
, Tomirotti
, M.
, and Valerio
, G.
, 2010
, “1923 Gleno Dam Break: Case Study and Numerical Modeling
,” J. Hydraulic Eng.
, 137
(4
), pp. 480
–492
. 10.1061/(ASCE)HY.1943-7900.000032721.
Seed
, H. B.
, and Duncan
, J. M.
, 1981
, “The Teton Dam Failure–A Retrospective Review
,” Soil Mechanics and Foundation Engineering: Proceedings of the 10th International Conference on soil Mechanics and Foundation Engineering
, Stockholm, Sweden
, June 15–19
, pp. 219
–238
.22.
Jayasuriya
, S. K.
, and McCawley
, P.
, 2011
, The Asian Tsunami: Aid and Reconstruction After a Disaster
, vol. 1
, Edward Elgar Publishing
, pp. 1
–272
.23.
West
, M.
, Sánchez
, J. J.
, and McNutt
, S. R.
, 2005
, “Periodically Triggered Seismicity At Mount Wrangell, Alaska, After the Sumatra Earthquake
,” Science
, 308
(5725
), pp. 1144
–1146
. 10.1126/science.111246224.
Ritter
, A.
, 1892
, “Die Fortpflanzung Der Wasserwellen
,” Zeitschrift des Vereines Deutscher Ingenieure
, 36
(33
), pp. 947
–954
.25.
Hu
, C.
, and Kashiwagi
, M.
, 2004
, “A CIP-Based Method for Numerical Simulations of Violent Free-Surface Flows
,” J. Mar. Sci. Technol.
, 9
(4
), pp. 143
–157
. 10.1007/s00773-004-0180-z26.
Zhou
, Z.
, De Kat
, J.
, and Buchner
, B.
, 1999
, “A Nonlinear 3D Approach to Simulate Green Water Dynamics on Deck
,” Proceedings of the Seventh International Conference on Numerical Ship Hydrodynamics
, Nantes, France
, July 1
, pp. 1
–15
.27.
Kleefsman
, K.
, Fekken
, G.
, Veldman
, A.
, Iwanowski
, B.
, and Buchner
, B.
, 2005
, “A Volume-of-Fluid Based Simulation Method for Wave Impact Problems
,” J. Comput. Phys.
, 206
(1
), pp. 363
–393
. 10.1016/j.jcp.2004.12.00728.
Wemmenhove
, R.
, Gladsø
, R.
, Iwanowski
, B.
, and Lefranc
, M.
, 2010
, “Comparison of CFD Calculations and Experiment for the Dambreak Experiment With One Flexible Wall
,” The Twentieth International Offshore and Polar Engineering Conference
, Beijing, China
, June 20–25
, International Society of Offshore and Polar Engineers
, pp. 200
–205
.29.
Lobovskỳ
, L.
, Botia-Vera
, E.
, Castellana
, F.
, Mas-Soler
, J.
, and Souto-Iglesias
, A.
, 2014
, “Experimental Investigation of Dynamic Pressure Loads During Dam Break
,” J. Fluids Struct.
, 48
, pp. 407
–434
. 10.1016/j.jfluidstructs.2014.03.00930.
Ertekin
, R. C.
, Hayatdavoodi
, M.
, and Kim
, J. W.
, 2014
, “On Some Solitary and Cnoidal Wave Diffraction Solutions of the Green-Naghdi Equations
,” Appl. Ocean Res.
, 47
, pp. 125
–137
. 10.1016/j.apor.2014.04.00531.
Robison
, J.
, and Scott Russell
, J.
, 1837
, “Report of the Committee on Waves
,” 7th Meeting of the British Association for the Advancement of Science
, Liverpool, UK
, May 4
, p. 226
.32.
Lighthill
, M. J.
, and Lighthill
, J.
, 1978
, Waves in Fluids
, Cambridge University Press
, New York
.33.
Stoker
, J. J.
, 1957
, Water Waves: The Nathematical Theory With Applications
, Vol. 36
, John Wiley & Sons
, New York
.34.
Johnson
, R. S.
, 1997
, A Modern Introduction to the Mathematical Theory of Water Waves
, Vol. 19
, Cambridge University Press
, New York
.35.
Craig
, W.
, 2002
, “Non-Eexistence of Solitary Water Waves in Three Dimensions
,” Philos. Trans. R. Soc. London, Ser. A.
, 360
(1799
), pp. 2127
–2135
. 10.1098/rsta.2002.106536.
Evans
, W.
, and Ford
, M.
, 1996
, “An Exact Integral Equation for Solitary Waves (With New Numerical Results for Some ‘Internal’ Properties)
,” Proc. R. Soc. London. Ser. A: Math., Phys. Eng. Sci.
, 452
(1945
), pp. 373
–390
. 10.1098/rspa.1996.002037.
Tsai
, C.-H.
, Huang
, M.-C.
, Young
, F.-J.
, Lin
, Y.-C.
, and Li
, H.-W.
, 2005
, “On the Recovery of Surface Wave by Pressure Transfer Function
,” Ocean Eng.
, 32
(10
), pp. 1247
–1259
. 10.1016/j.oceaneng.2004.10.02038.
Escher
, J.
, and Schlurmann
, T.
, 2008
, “On the Recovery of the Free Surface From the Pressure Within Periodic Traveling Water Waves
,” J. Nonlinear Math. Phys.
, 15
(suppl 2
), pp. 50
–57
. 10.2991/jnmp.2008.15.s2.439.
Constantin
, A.
, Escher
, J.
, and Hsu
, H.-C.
, 2011
, “Pressure Beneath a Solitary Water Wave: Mathematical Theory and Experiments
,” Arch. Rational Mech. Anal.
, 201
(1
), pp. 251
–269
. 10.1007/s00205-011-0396-040.
Ferziger
, J. H.
, and Peric
, M.
, 2012
, Computational Methods for Fluid Dynamics
, Vol. 3
, Springer Science & Business Media
, Berlin
.41.
Menter
, F. R.
, 1993
, “Zonal Two Equation k − ε Turbulence Models for Aerodynamic Flows
,” 23rd Fluid Dynamics, Plasmadynamics, and Lasers Conference
, Orlando, FL
, July 6–9
, pp. 1
–21
.42.
Menter
, F. R.
, Kuntz
, M.
, and Langtry
, R.
, 2003
, “Ten Years of Industrial Experience With the SST Turbulence Model
,” Turbulence, Heat Mass Transfer
, 4
(1
), pp. 625
–632
.43.
Wilcox
, D. C.
, 1998
, Turbulence modeling for CFD
, Vol. 2
, DCW Industries
, La Canada, CA
.44.
Mokrani
, C.
, and Abadie
, S.
, 2016
, “Conditions for Peak Pressure Stability in VOF Simulations of Dam Break Flow Impact
,” J. Fluids Struct.
, 62
, pp. 86
–03
. 10.1016/j.jfluidstructs.2015.12.00745.
Hirt
, C. W.
, and Nichols
, B. D.
, 1981
, “Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,” J. Comput. Phys.
, 39
(1
), pp. 201
–225
. 10.1016/0021-9991(81)90145-546.
Greenshields
, C. J.
, 2018
, “OpenFOAM User Guide
,” OpenFOAM Foundation Ltd
, version, 3
(1
).47.
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
, pp. 102
–118
. 10.1016/j.coastaleng.2012.07.00248.
Green
, A. E.
, Laws
, N.
, and Naghdi
, P. M.
, 1974
, “On the Theory of Water Waves
,” Proc. R. Soc. Lond. A
, 338
(1612
), pp. 43
–55
. 10.1098/rspa.1974.007249.
Green
, A. E.
, and Naghdi
, P. M.
, 1976
, “Directed Fluid Sheets
,” Proc. R. Soc. London
, 347
(1651
), pp. 447
–473
. 10.1098/rspa.1976.001150.
Green
, A. E.
, and Naghdi
, P. M.
, 1976
, “A Derivation of Equations for Wave Propagation in Water of Variable Depth
,” J. Fluid Mech.
, 78
(2
), pp. 237
–246
. 10.1017/S002211207600242551.
Ertekin
, R. C.
, 1984
, “Soliton Generation by Moving Disturbances in Shallow Water: Theory, Computation and Experiment
,” Ph.D. thesis, University of California
at Berkeley
.52.
Hayatdavoodi
, M.
, and Ertekin
, R. C.
, 2015
, “Nonlinear Wave Loads on a Submerged Deck by the Green–Naghdi Equations
,” ASME J. Offshore Mech. Arct. Eng.
, 137
(1
), p. 011102
. 10.1115/1.402899753.
Hayatdavoodi
, M.
, and Ertekin
, R. C.
, 2015
, “Wave Forces on a Submerged Horizontal Plate. Part I: Theory and Modelling
,” J. Fluids Struct.
, 54
(April
), pp. 566
–579
. 10.1016/j.jfluidstructs.2014.12.01054.
Hayatdavoodi
, M.
, and Ertekin
, R. C.
, 2015
, “Wave Forces on a Submerged Horizontal Plate. Part II: Solitary and Cnoidal Waves
,” J. Fluids Struct.
, 54
(April
), pp. 580
–596
. 10.1016/j.jfluidstructs.2014.12.00955.
Hayatdavoodi
, M.
, Ertekin
, R. C.
, and Valentine
, B. D.
, 2017
, “Solitary and Cnoidal Wave Scattering by a Submerged Horizontal Plate in Shallow Water
,” AIP Adv.
, 7
(6
), p. 065212
. 10.1063/1.498702456.
Neill
, D. R.
, Hayatdavoodi
, M.
, and Ertekin
, R. C.
, 2018
, “On Solitary Wave Diffraction by Multiple, In-Line Vertical Cylinders
,” Nonlinear Dyn.
, 91
(2
), pp. 975
–994
. 10.1007/s11071-017-3923-157.
Hayatdavoodi
, M.
, Neill
, D. R.
, and Ertekin
, R. C.
, 2018
, “Diffraction of Cnoidal Waves by Vertical Cylinders in Shallow Water
,” Theor. Comput. Fluid Dyn.
, 32
(5
), pp. 561
–591
. 10.1007/s00162-018-0466-058.
Zhao
, B. B.
, Duan
, W. Y.
, and Ertekin
, R. C.
, 2014
, “Application of Higher-Level GN Theory to Some Wave Transformation Problems
,” Coastal Eng.
, 83
(1
), pp. 177
–189
. 10.1016/j.coastaleng.2013.10.01059.
Zhao
, B. B.
, Ertekin
, R. C.
, Duan
, W. Y.
, and Hayatdavoodi
, M.
, 2014
, “On the Steady Solitary-Wave Solution of the Green–Naghdi Equations of Different Levels
,” Wave Motion
, 51
(8
), pp. 1382
–1395
. 10.1016/j.wavemoti.2014.08.00960.
Zhao
, B. B.
, Duan
, W. Y.
, Ertekin
, R. C.
, and Hayatdavoodi
, M.
, 2015
, “High-Level Green–Naghdi Wave Models for Nonlinear Wave Transformation in Three Dimensions
,” J. Ocean Eng. Mar. Energy
, 1
(2
), pp. 121
–132
. 10.1007/s40722–014–0009–861.
Saint-Venant
, A. D.
, 1871
, “Theorie Du Mouvement Non Permanent Des Eaux, Avec Application Aux Crues Des Rivieres Et a Líntroduction De Marees Dans Leurs Lits
,” Comptes rendus des seances de l ′ Academie des Sciences
, 36
, pp. 147
–237
. 10.3406/crai.1914.7340762.
Mises
, R. V.
, 1945
, “On Saint Venant’s Principle
,” Bull. Am. Math. Soc.
, 51
(8
), pp. 555
–562
. 10.1090/S0002-9904-1945-08394-363.
Manning
, R.
, 1889
, “On the Flow of Water in Open Channels and Pipes
,” Inst. Civil Eng. Ireland
, 20
, pp. 161
–207
.64.
Kundu
, P.
, and Cohen
, L.
, 1990
, Fluid Mechanics
, Academic Press
, San Diego, CA
.65.
Jameson
, A.
, Schmidt
, W.
, and Turkel
, E.
, 1981
, “Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge Kutta Time Stepping Schemes
,” 14th Fluid and Plasma Dynamics Conference
, Palo Alto, CA
, June 23–25
, p. 1259
.66.
Issa
, R. I.
, 1986
, “Solution of the Implicitly Discretised Fluid Flow Equations by Operator-splitting
,” J. Comput. Phys.
, 62
(1
), pp. 40
–65
. 10.1016/0021-9991(86)90099-967.
Holzmann
, T.
, 2016
, Mathematics, Numerics, Derivations and Openfoam®
, Loeben, Germany
, Holzmann CFD
.68.
Ertekin
, R. C.
, Webster
, W. C.
, and Wehausen
, J. V.
, 1986
, “Waves Caused by a Moving Disturbance in a Shallow Channel of Finite Width
,” J. Fluid Mech.
, 169
, pp. 275
–292
. 10.1017/S002211208600063069.
Morris
, A. G.
, 2013
, “Adapting Cartesian Cut Cell Methods for Flood Risk Evaluation
,” Ph.D. thesis, Manchester Metropolitan University
.70.
Hayatdavoodi
, M.
, Seiffert
, B.
, and Ertekin
, R. C.
, 2015
, “Experiments and Calculations of Cnoidal Wave Loads on a Flat Plate in Shallow-Water
,” J. Ocean Eng. Mar. Energy
, 1
(1
), pp. 77
–99
. 10.1007/s40722–014–0007–x71.
Hayatdavoodi
, M.
, Treichel
, K.
, and Ertekin
, R. C.
, 2019
, “Parametric Study of Nonlinear Wave Loads on Submerged Decks in Shallow Water
,” J. Fluids Struct.
, 86
, pp. 266
–289
. 10.1016/j.jfluidstructs.2019.02.016Copyright © 2019 by ASME
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