A Comparative Study of Numerical Models for Wave Propagation and Setup on Steep Coral Reefs
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摘要
Complex factors including steep slopes, intense wave breaking, large bottom friction and remarkable wave setup should be considered while studying wave propagation over coral reefs, and how to simulate wave propagation and setup on coral reefs efficiently has become a primary focus. Several wave models can be used on coral reefs as have been published, but further testing and comparison of the reliability and applicability of these models are needed. A comparative study of four numerical wave models(i.e., FUNWAVE-TVD, Coulwave, NHWAVE and ZZL18) is carried out in this paper. These models' governing equations and numerical methods are compared and analyzed firstly to obtain their differences and connections; then the simulation effects of the four wave models are tested in four representative laboratory experiments. The results show that all four models can reasonably predict the spectrum transformation. Coulwave, NHWAVE and ZZL18 can predict the wave height variation more accurately; Coulwave and FUNWAVE-TVD tend to underestimate wave setup on the reef top induced by spilling breaker, while NHWAVE and ZZL18 can predict wave setup relatively accurately for all types of breakers; NHWAVE and ZZL18 can predict wave reflection by steep reef slope more accurately. This study can provide evidence for choosing suitable models for practical engineering or establishing new models.
Complex factors including steep slopes, intense wave breaking, large bottom friction and remarkable wave setup should be considered while studying wave propagation over coral reefs, and how to simulate wave propagation and setup on coral reefs efficiently has become a primary focus. Several wave models can be used on coral reefs as have been published, but further testing and comparison of the reliability and applicability of these models are needed. A comparative study of four numerical wave models(i.e., FUNWAVE-TVD, Coulwave, NHWAVE and ZZL18) is carried out in this paper. These models' governing equations and numerical methods are compared and analyzed firstly to obtain their differences and connections; then the simulation effects of the four wave models are tested in four representative laboratory experiments. The results show that all four models can reasonably predict the spectrum transformation. Coulwave, NHWAVE and ZZL18 can predict the wave height variation more accurately; Coulwave and FUNWAVE-TVD tend to underestimate wave setup on the reef top induced by spilling breaker, while NHWAVE and ZZL18 can predict wave setup relatively accurately for all types of breakers; NHWAVE and ZZL18 can predict wave reflection by steep reef slope more accurately. This study can provide evidence for choosing suitable models for practical engineering or establishing new models.
Complex factors including steep slopes, intense wave breaking, large bottom friction and remarkable wave setup should be considered while studying wave propagation over coral reefs, and how to simulate wave propagation and setup on coral reefs efficiently has become a primary focus. Several wave models can be used on coral reefs as have been published, but further testing and comparison of the reliability and applicability of these models are needed. A comparative study of four numerical wave models(i.e., FUNWAVE-TVD, Coulwave, NHWAVE and ZZL18) is carried out in this paper. These models' governing equations and numerical methods are compared and analyzed firstly to obtain their differences and connections; then the simulation effects of the four wave models are tested in four representative laboratory experiments. The results show that all four models can reasonably predict the spectrum transformation. Coulwave, NHWAVE and ZZL18 can predict the wave height variation more accurately; Coulwave and FUNWAVE-TVD tend to underestimate wave setup on the reef top induced by spilling breaker, while NHWAVE and ZZL18 can predict wave setup relatively accurately for all types of breakers; NHWAVE and ZZL18 can predict wave reflection by steep reef slope more accurately. This study can provide evidence for choosing suitable models for practical engineering or establishing new models.
引文
Buckley,M.,Lowe,R.and Hansen,J.,2014.Evaluation of nearshore wave models in steep reef environments,Ocean Dynamics,64(6),847-862.
Buckley,M.L.,Lowe,R.J.,Hansen,J.E.and Van Dongeren,AR.,2015.Dynamics of wave setup over a steeply sloping fringing reef,Journal of Physical Oceanography,45(12),3005-3023.
Demirbilek,Z.,Nwogu,O.G.and Ward,D.L.,2007.Laboratory Study of Wind Effect on Runup Over Fringing reefs,Report 1,Data Rep,US Amry Corps of Engineering,UAA.
Fang,K.Z.,Liu,Z.B.and Zou,Z.L.,2016.Fully nonlinear modeling wave transformation over fringing reefs using shock-capturing boussinesq model,Journal of Coastal Research,32(1),164-171.
Gallagher,E.L.,Elgar,S.and Guza,R.T.,1998.Observations of sand bar evolution on a natural beach,Journal of Geophysical Research:Oceans,103(C2),3203-3215.
Gourlay,M.R.,1996.Wave set-up on coral reefs.1.Set-up and wavegenerated flow on an idealised two dimensional horizontal reef,Coastal Engineering,27(3-4),161-193.
Kazolea,M.,Filippini,A.G.,Ricchiuto,M.,Abadie,S.,Medina,M.M.,Morichon,D.,Journeau,C.,Marcer,R.,Pons,K.,Le Roy,S.,Pedreros,R.and Rousseau,M.,2016.Wave Propagation Breaking,and Overtoping on A 2D Reef:A Comparative Evaluation of Numerical Codes for Tsunami Modelling,Research Report RR-9005,Inria.
Kazolea,M.and Ricchiuto,M.,2018.On wave breaking for Boussinesq-type models,Ocean Modelling,123,16-39.
Kennedy,A.B.,Chen,Q.,Kirby,J.T.and Dalrymple,R.A.,2000.Boussinesq modeling of wave transformation,breaking,and runup.I:1D,Journal of Waterway,Port,Coastal,and Ocean Engineering,126(1),39-47.
Kennedy,A.B.,Kirby,J.T.,Chen,Q.and Dalrymple,R.A.,2001.Boussinesq-type equations with improved nonlinear performance,Wave Motion,33(3),225-243.
Kim,G.,Lee,C.and Suh,K.D.,2009.Extended Boussinesq equations for rapidly varying topography,Ocean Engineering,36(11),842-851.
Lynett,P.J.,Liu,P.L.F.,Sitanggang,K.I.and Kim,D.H.,2008.Modeling Wave Generation,Evolution,and Interaction with Depth-Integrated,Dispersive Wave Equations COULWAVE Code Manual,Cornell University Long and Intermediate Wave Modeling Package v.2.0,USA.
Ma,G.F.,Shi,F.Y.and Kirby,J.T.,2012.Shock-capturing non-hydrostatic model for fully dispersive surface wave processes,Ocean Modelling,43-44,22-35.
Ma,G.F.,Su,S.F.,Liu,S.G.and Chu,J.C.,2014.Numerical simulation of infragravity waves in fringing reefs using a shock-capturing non-hydrostatic model,Ocean Engineering,85,54-64.
Metallinos,A.S.,Repousis,E.G.and Memos,C.D.,2016.Wave propagation over a submerged porous breakwater with steep slopes,Ocean Engineering,111,424-438.
Roeber,V.and Cheung,K.F.,2012.Boussinesq-type model for energetic breaking waves in fringing reef environments,Coastal Engineering,70,1-20.
Sheremet,A.,Kaihatu,J.M.,Su,S.F.,Smith,E.R.and Smith,J.M.,2011.Modeling of nonlinear wave propagation over fringing reefs,Coastal Engineering,58(12),1125-1137.
Shi,F.Y.,Kirby,J.T.,Harris,J.C.,Geiman,J.D.and Grilli,S.T.,2012a.A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation,Ocean Modelling,43-44,36-51.
Shi,F.Y.,Kirby,J.T.,Tehranirad,B.,Harris,J.C.and Grilli,S.,2012b.FUNWAVE-TVD Fully Nonlinear Boussinesq Wave Model with TVD Solver Documentation and User’s Manual(Version 2.0),University of Delaware,Center for Applied Coastal Research,Newark Delaware.
Skotner,C.and Apelt,C.J.,1999.Application of a Boussinesq model for the computation of breaking waves:Part 2:Wave-induced setdown and setup on a submerged coral reef,Ocean Engineering,26(10),927-947.
Smith,E.R.,Hesser,T.and Smith,J.M.,2012.Two-and Three-Dimensional Laboratory Studies of Wave Breaking,Setup,and Runup on Reefs,Dissipation,US Amry Corps of Engineering,UAA.
Su,S.F.,Ma,G.F.and Hsu,T.W.,2015.Boussinesq modeling of spatial variability of infragravity waves on fringing reefs,Ocean Engineering,101,78-92.
Wei,G.,Kirby,J.T.,Grilli,S.T.and Subramanya,R.,1995.A fully nonlinear Boussinesq model for surface waves.Part I.Highly nonlinear unsteady waves,Journal of Fluid Mechanics,294,71-92.
Wen,H.J.,Ren,B.,Zhang,X.and Yu,X.P.,2019.SPH modeling of wave transformation over a coral reef with seawall,Journal of Waterway,Port,Coastal,and Ocean Engineering,145(1),04018026.
Yao,Y.,Huang,Z.H.,Monismith,S.G.and Lo,E.Y.M.,2012.1DHBoussinesq modeling of wave transformation over fringing reefs,Ocean Engineering,47,30-42.
Zhang,S.J.,Zhu,L.S.and Li,J.H.,2018.Numerical simulation of wave propagation,breaking,and setup on steep fringing reefs,Water,10(9),1147.
Zhu,L.S.and Hong,G.W.,2001.Numerical calculation for nonlinear waves in waterof arbitrarily varying depth with boussinesq equations,China Ocean Engineering,15(3),355-369.
Zhu,L.S.,Li,M.Q.,Zhang,H.S.and Sui,S.F.,2004.Wave attenuation and friction coefficient on the coral-reef flat,China Ocean Engineering,18(1),129-136.
Zijlema,M.,2012.Modelling wave transformation across a fringing reef using swash,Proceedings of the 33rd Conference on Coastal Engineering,Coastal Engineering Research Council,Singapore,Spain.
Zou,Z.L.and Fang,K.Z.,2008.Alternative forms of the higher-order Boussinesq equations:Derivations and validations,Coastal Engineering,55(6),506-521.
Buckley,M.L.,Lowe,R.J.,Hansen,J.E.and Van Dongeren,AR.,2015.Dynamics of wave setup over a steeply sloping fringing reef,Journal of Physical Oceanography,45(12),3005-3023.
Demirbilek,Z.,Nwogu,O.G.and Ward,D.L.,2007.Laboratory Study of Wind Effect on Runup Over Fringing reefs,Report 1,Data Rep,US Amry Corps of Engineering,UAA.
Fang,K.Z.,Liu,Z.B.and Zou,Z.L.,2016.Fully nonlinear modeling wave transformation over fringing reefs using shock-capturing boussinesq model,Journal of Coastal Research,32(1),164-171.
Gallagher,E.L.,Elgar,S.and Guza,R.T.,1998.Observations of sand bar evolution on a natural beach,Journal of Geophysical Research:Oceans,103(C2),3203-3215.
Gourlay,M.R.,1996.Wave set-up on coral reefs.1.Set-up and wavegenerated flow on an idealised two dimensional horizontal reef,Coastal Engineering,27(3-4),161-193.
Kazolea,M.,Filippini,A.G.,Ricchiuto,M.,Abadie,S.,Medina,M.M.,Morichon,D.,Journeau,C.,Marcer,R.,Pons,K.,Le Roy,S.,Pedreros,R.and Rousseau,M.,2016.Wave Propagation Breaking,and Overtoping on A 2D Reef:A Comparative Evaluation of Numerical Codes for Tsunami Modelling,Research Report RR-9005,Inria.
Kazolea,M.and Ricchiuto,M.,2018.On wave breaking for Boussinesq-type models,Ocean Modelling,123,16-39.
Kennedy,A.B.,Chen,Q.,Kirby,J.T.and Dalrymple,R.A.,2000.Boussinesq modeling of wave transformation,breaking,and runup.I:1D,Journal of Waterway,Port,Coastal,and Ocean Engineering,126(1),39-47.
Kennedy,A.B.,Kirby,J.T.,Chen,Q.and Dalrymple,R.A.,2001.Boussinesq-type equations with improved nonlinear performance,Wave Motion,33(3),225-243.
Kim,G.,Lee,C.and Suh,K.D.,2009.Extended Boussinesq equations for rapidly varying topography,Ocean Engineering,36(11),842-851.
Lynett,P.J.,Liu,P.L.F.,Sitanggang,K.I.and Kim,D.H.,2008.Modeling Wave Generation,Evolution,and Interaction with Depth-Integrated,Dispersive Wave Equations COULWAVE Code Manual,Cornell University Long and Intermediate Wave Modeling Package v.2.0,USA.
Ma,G.F.,Shi,F.Y.and Kirby,J.T.,2012.Shock-capturing non-hydrostatic model for fully dispersive surface wave processes,Ocean Modelling,43-44,22-35.
Ma,G.F.,Su,S.F.,Liu,S.G.and Chu,J.C.,2014.Numerical simulation of infragravity waves in fringing reefs using a shock-capturing non-hydrostatic model,Ocean Engineering,85,54-64.
Metallinos,A.S.,Repousis,E.G.and Memos,C.D.,2016.Wave propagation over a submerged porous breakwater with steep slopes,Ocean Engineering,111,424-438.
Roeber,V.and Cheung,K.F.,2012.Boussinesq-type model for energetic breaking waves in fringing reef environments,Coastal Engineering,70,1-20.
Sheremet,A.,Kaihatu,J.M.,Su,S.F.,Smith,E.R.and Smith,J.M.,2011.Modeling of nonlinear wave propagation over fringing reefs,Coastal Engineering,58(12),1125-1137.
Shi,F.Y.,Kirby,J.T.,Harris,J.C.,Geiman,J.D.and Grilli,S.T.,2012a.A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation,Ocean Modelling,43-44,36-51.
Shi,F.Y.,Kirby,J.T.,Tehranirad,B.,Harris,J.C.and Grilli,S.,2012b.FUNWAVE-TVD Fully Nonlinear Boussinesq Wave Model with TVD Solver Documentation and User’s Manual(Version 2.0),University of Delaware,Center for Applied Coastal Research,Newark Delaware.
Skotner,C.and Apelt,C.J.,1999.Application of a Boussinesq model for the computation of breaking waves:Part 2:Wave-induced setdown and setup on a submerged coral reef,Ocean Engineering,26(10),927-947.
Smith,E.R.,Hesser,T.and Smith,J.M.,2012.Two-and Three-Dimensional Laboratory Studies of Wave Breaking,Setup,and Runup on Reefs,Dissipation,US Amry Corps of Engineering,UAA.
Su,S.F.,Ma,G.F.and Hsu,T.W.,2015.Boussinesq modeling of spatial variability of infragravity waves on fringing reefs,Ocean Engineering,101,78-92.
Wei,G.,Kirby,J.T.,Grilli,S.T.and Subramanya,R.,1995.A fully nonlinear Boussinesq model for surface waves.Part I.Highly nonlinear unsteady waves,Journal of Fluid Mechanics,294,71-92.
Wen,H.J.,Ren,B.,Zhang,X.and Yu,X.P.,2019.SPH modeling of wave transformation over a coral reef with seawall,Journal of Waterway,Port,Coastal,and Ocean Engineering,145(1),04018026.
Yao,Y.,Huang,Z.H.,Monismith,S.G.and Lo,E.Y.M.,2012.1DHBoussinesq modeling of wave transformation over fringing reefs,Ocean Engineering,47,30-42.
Zhang,S.J.,Zhu,L.S.and Li,J.H.,2018.Numerical simulation of wave propagation,breaking,and setup on steep fringing reefs,Water,10(9),1147.
Zhu,L.S.and Hong,G.W.,2001.Numerical calculation for nonlinear waves in waterof arbitrarily varying depth with boussinesq equations,China Ocean Engineering,15(3),355-369.
Zhu,L.S.,Li,M.Q.,Zhang,H.S.and Sui,S.F.,2004.Wave attenuation and friction coefficient on the coral-reef flat,China Ocean Engineering,18(1),129-136.
Zijlema,M.,2012.Modelling wave transformation across a fringing reef using swash,Proceedings of the 33rd Conference on Coastal Engineering,Coastal Engineering Research Council,Singapore,Spain.
Zou,Z.L.and Fang,K.Z.,2008.Alternative forms of the higher-order Boussinesq equations:Derivations and validations,Coastal Engineering,55(6),506-521.