NONLINEAR(PROPAGATION(OF(STORM(WAVES:( INFRAGRAVITY(WAVE(GENERATION(AND(DYNAMICS((

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1 PanQAmericanAdvancedStudiesInsLtute TheScienceofPredicLngandUnderstandingTsunamis,Storm SurgesandTidalPhenomena BostonUniversity MechanicalEngineering NONLINEARPROPAGATIONOFSTORMWAVES: INFRAGRAVITYWAVEGENERATIONANDDYNAMICS AssociateProfessor HydraulicandEnvironmentalEngineeringDepartment PonLficiaUniversidadCatólicadeChile DeputyDirector NaLonalResearchCenterforIntegratedNaturalDisastersManagement h"p:// Associated/NaHonal/UniversiHes/ Excellence/Research/Center/funded/by/CONICYT/ Fondap/2011/

2 PanQAmericanAdvancedStudiesInsLtute TheScienceofPredicLngandUnderstandingTsunamis,Storm SurgesandTidalPhenomena BostonUniversity MechanicalEngineering I.MoLvaLon PRESENTATIONOUTLINE II.NonlinearWavePropagaLonintheNearshore III.ANumericalandExperimentalStudyonInfragravityWaves IV.ChileasanInternaLonalNaturalCoastalLaboratory

3 I.MOTIVATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 ThenumberofNDhaveskyrocketedoverthelastcentury ThenumberofaffectedpeopleandesLmateddamagefollowthe trend Thenumberofdeadpeopledecouplesfromthetrend Source:EMQDATInternaLonalDisastersDatabase CREDQh`p://

4 I.MOTIVATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 Extreme,largeandrapidflooding Tsunamis,/flash/floods,/GLOF,/storm/waves/ Significantconsequences Human/lives/ FaciliHes/and/structures/ Social/and/environmental/impact/

5 I.MOTIVATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 RecentLargeRiver FloodsinChile Chaitén,/2008/ Talca,/2008/ BíoBío,/2006/ Licantén,/2008/ 5/ Mapocho,/1982/

6 I.MOTIVATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 RecentGlacialLakeOutburstFloodsinChile / GLOF/in/the/Chilean/Patagonia/Chachet/2)/ More/than/6/episodes/since/april/2008/ 4.5m/stage/rise/and/3500m3/s/peak/discharge/ in/baker/river/in/less/than/48/hours./ / April/2008/ May/2008/ Glaciologia.cl/

7 I.MOTIVATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 RecentMajorTsunamis inchile Valdivia,1960 ConsHtución,/2010/ Pelluhue,/2010/

8 I.MOTIVATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 RecentMajorStormWaves inchile Source:ElMostrador h`p:// August16 th 2012

9 I.MOTIVATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 NonlinearwavesareinpermanentacLon,shapingour environment,andquesloningthewaythesocietyfitsinit WidetemporalandspaLalscales ComplexnonlinearinteracLons Strangeconsequences? AmazingresearchopportuniLesfor contribulngtotheunderstandingof theseprocessesandtheirconsequences Trucvertbeach,FrenchAtlanLcCoast CourtesyofP.LarroudéLEGI)

10 PanQAmericanAdvancedStudiesInsLtute TheScienceofPredicLngandUnderstandingTsunamis,Storm SurgesandTidalPhenomena BostonUniversity MechanicalEngineering I.MoLvaLon PRESENTATIONOUTLINE II.NonlinearWavePropagaLonintheNearshore III.ANumericalandExperimentalStudyonInfragravityWaves IV.ChileasanInternaLonalNaturalCoastalLaboratory

11 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 Shoaling, breakingand runqupofan incident laboratory wave Simplified 2DV viewofnearshore wavepropagalon Source:LaboratoryExperimentintheLEGIWaveFlume,France

12 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 Shoaling/zone/ Surf/zone/ /swash/ zone/ z z = ηx,t)# h 0 a L c H Nonlinearity Dispersion ε = a / h 0 σ = h / 0 L Long wave shallow water) models σ 0.1

13 II.NONLINEARWAVEPROPAGATION Wave merging in the inner surf zone Sénéchal, Dupuis, Bonneton 2001) PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 Higher harmonics release after a bar Sénéchal, Bonneton, Dupuis 2002)

14 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 Regularwavesshoalingoverasubmergedbar,andhigher harmonicsreleaseoncewaterdepthincreases GeneraLonofboundhigherharmonicsintheshoalshallowwater propagalon) Over intermediate depths,higherharmonicstravelattheir own speed Source:Cienfuegosetal.,2007;Dingemans,1994experiments

15 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 WavepropagaLoncreatesasetQdownandsetQupinthemeansealevel Fissionofthemainwavefrontforlongerperiodwaves Source:Cienfuegosetal.,2010;HansenandSvendsen,1979experiments

16 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 TsunamiwavefissionintheSendaiarea,Japan2011

17 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 SetQdown/SetQupovera uniformbeachunder regularwavepropagalon RadiaLonstressconceptfor waveqaveragedquanlles LonguetQHigginsand Stewart,1962) S xx x + ρg η + h ) η x = 0 ' S xx = E " # cos 2 θ +1$ % C g C 1 * + ) 2, Source:Bowenetal.,1968

18 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 InfragravitywaveIG)generaLonunderrandomwaveforcing LongwavesforcedbyhighQfrequencywavegroups 2ndOrderLongWaveGeneraLonMechanism NegaLvecorrelaLon betweengroup envelopeandig waves AdaptedformDeanand Dalrymple,1984 MeanwaterlevelpulsaLonassociatedtowavegroups setq up/setqdownlonguetqhigginsandstewart,1962) BoundlongwavespropagaLngatgroupvelocity

19 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 InfragravitywaveIG)generaLonunderrandomwaveforcing LongwavesforcedbyavariablebreakpointlocaLon TheslowmodulaLonofthebreakingpointunderarandomwavefield producesadynamicsetqup/setqdown AdaptedfromL.H.Holthuijsen,2007 PosiLvecorrelaLon betweengroupenvelope andigwaves SURFBEATSymonds,1982)!

20 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 PracLcalconsequencesofIGwaves:IncreasedrunQups RandomshortwavestransferenergytoinfragravitywaveswhilepropagaLngtowardsthe shore VeryimportantforswashzonedynamicsandmaximumobservedrunQups

21 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 PracLcalconsequencesofIGwaves:Edgewaves Trapped Edge Waves at Truc Vert Beach, France Thebreakingprocess isresponsibleforthe releaseofigwaves ~ 500m ~ 100m IGwavesreflectat thecoastswash) RefracLontrapsIG soqcallededgewaves)

22 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 PracLcalconsequencesofIGwaves:Edgewaves Incidentperiodicwaves: H=1m;T=100s;θ 0 =30 Uniformbeachprofile: h 0 =10;s=1/40 Reflectedwavesare trappedandpropagatein thealongshoredireclon Importantconsequences formaximunrunqup distribulon NSWEFVmodeldeveloped bym.guerrapucmsc thesis) NumericalsimulaLonby JoséGalazPUCundergrad student)

23 II.NONLINEARWAVEPROPAGATION PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 PracLcalconsequencesofIGwaves?RipinstabiliLes Frontalincidentrandomwave trainswithasmallamplitude perturbaloninthecenter RipcurrentgeneraLon SlowmeancurrentpulsaLons QuasiQperiodicejecLonofdriters PhDthesisofLeandroSuarezPUCQLEGIgradstudent) Suarezetal.,ICCE2012;Suarezetal.,CD2013

24 PanQAmericanAdvancedStudiesInsLtute TheScienceofPredicLngandUnderstandingTsunamis,Storm SurgesandTidalPhenomena BostonUniversity MechanicalEngineering I.MoLvaLon PRESENTATIONOUTLINE II.NonlinearWavePropagaLonintheNearshore III.ANumericalandExperimentalStudyonInfragravityWaves IV.ChileasanInternaLonalNaturalCoastalLaboratory

25 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 Different methods to cope & understand water waves Source: P. Bonneton, 2010

26 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 General Definitions and Framework L!c! z! x! H!!!z=η! MWL! SWL! a Arbitrarybo`om bathymetry Incompressibleandinviscid fluid z=ξ! h! h 0 QuasiQIrrotaLonalflow

27 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 NonQdimensionaldepthQaveragedmassandmomentumequaLons h t +ε[ hu ] = 0 x Nonlinearity ε = a / h 0 [ ] t + h εu2 + p ε hu [ )] x + ξ x p ξ = 0 Dispersion σ = h / 0 L Wherethepressurefieldiswri`enas: px,z,t) = εη z εη ) +εσ 2 Γ x,z,t z )dz andthefunclonγrepresentstheverlcalacceleralonoffluidparlcles: Dw & 1 Γ x, z, t) = = wt + ε$ uwx + 2 Dt % σ ww z #! "

28 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 UsingapproximateexpressionsforthevelocityfieldpotenLalflowtheory)weget thefullynonlinearweaklydispersiveserre/greenqnaghdiequalonscienfuegoset al.,2006;lannesandbonneton,2009) h [ hu] = 0 t + ε x ) 2 ) 2 2 hu + ε hu + h h + ξ ) + σ h P x, t) + Q x, t) + t Where: P Q x ) 2 x t = h u + εuu εu ), xt xx x 2 x, t) = ξ u + εuu ) + εξ u x t x x xx & % $, 1 * σ ξ h& P ' )# '"! ) ) 4 x, t + Q x, t O σ ) x # = Droppingoverbarsforsimplicity x % $

29 PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 III.INFRAGRAVITYWAVES A4thOrderFVS/GQNModelCienfuegosetal.,2006,2007) AstronglynonlinearandweaklydispersiveBoussinesqsystemOσ 4 )!! " # = + = x t x t G q F h ) ) ) ) ) ) xx x x x x x x x x x h h r u h h u r q hu u hu u h g uq G hu F ξ ξ ξ ξ ξ ξ = + = = = WiththefollowingdefiniLonsforfluxfuncLonsandauxiliaryvariables

30 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 IncorporaLngBreakingEnergyDissipaLonMignotandCienfuegos, 2009;Cienfuegosetal.,2010) DiffusiveQliketermsinboth,massandmomentumconservaLonequaLons $ h! #! q " t t + F x + G x + + D 1 h h D h = ν h h ) x x = D hu D hu = ν hu hu) x 0 = [ ] x 0 Local redistribution of mass and momentum below breakers Diffusivity function Similar to Kennedy et al., 2000

31 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 nonlinear processes L.H.Holthuijsen,2007 TypicalwindQgeneratedwaves:0.05Hz20s) 1Hz1s) Nonlinearprocessesshoaling,breaking,swash)generate infragravityig)waves:0.001hz1000s) 0.05Hz20s)

32 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 ExperimentalInvesLgaLonattheInsLtutoNacionaldeHidráulica 70m long x 1.5m wide x 1.5m deep wave tank Piston wave paddle with active absorption DHI) Resistive probes for free surface measurements Sontek MicroADV for velocity measurements Very mild slope beach 1/80

33 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 RandomIncidentWaveField Jonswap spectrum Hasselmann, 1973) for incident wave field Tp=4 s 0.25Hz) ; H mo =18 cm ; h 0 =52cm Without phase structure uniform random distribution [0,2π]) Highly nonlinear shallow water regime Althoughtheforcingwavefielddoes notcontainenergyintheinfragravity band,experimentsshowimportant energycontentatthesefrequencies

34 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 SeparaLonofIncidentandReflectedWaves Radon transform Deans, 1983) in time domain to separate incident and reflected signals Almar et al., 2013) Total Incident Reflected Freesurface Lmestacks Freesurface atx=20m Amplitude evolulon

35 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 ModelPerformanceonHighFrequencyWaves Total/ Waveheight andenergy distribulon 1 st /harmonic/ 2 nd /harmonic/ CrestQtroughwave asymmetrysk) LetQrightwave symmetryas)

36 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 SpectralEnergyEvoluLonAlongtheExperimentalFlume x=-22m x =-22[m] x=-9m x =-9[m] Ef) [m 2 /Hz] 10-5 Ef) [m 2 /Hz] x=0m x =0[m] x=9m x =9[m] Ef) [m 2 /Hz] x=20m x =20[m] x=32m x =32[m] Ef) [m 2 /Hz] fhz) Partial reflection at the wave paddle produces low frequency selection in the flume fhz) Natural modes f 1 =0.013Hz f 2 =0.023Hz f 3 =0.031Hz

37 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 ModelPerformanceinSpectralEnergyEvoluLon x =-22[m] x =-9[m] Ef) [m 2 /Hz] 10-5 Ef) [m 2 /Hz] x =0[m] x =9[m] Blue: Experiments Red : Model Ef) [m 2 /Hz] x =20[m] x =32[m] Ef) [m 2 /Hz] fhz) fhz) ThemodelsucceedsintransferringenergytohigherharmonicsandIG wavesbutnoclearmodalseleclonopenboundarycondilon)

38 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 CrossQcorrelaLonmapsbetweengroupamplitudeandIGwave amplitudeateachlocalon Experimental Numerical

39 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 CrossQcorrelaLonmapsbetweengroupamplitudeatthefirstgauge andigwaveamplitudeateachlocalon Experimental Numerical

40 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 A bound IG appears rapidly in the shoaling zone forced by short wave groups negative correlation slightly lagging the group) A positive long wave surge preceding the group develops as the short waves propagate towards the shore positive correlation running ahead of the group) There is a phase shift for the positively correlated IG wave in the inner surf zone Both IG waves appear to be partially reflected on run-up some dissipation by breaking might occur)

41 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 The shallow water regime Cg~C) produces a nearly resonant condition for IG wave forcing Nielsen and Baldock, 2010) pffiffiffiffiffi pffiffiffiffiffi ThesoQcalledNQshapedlongwaveisforcedasaboundwaveintheshoaling zone pffiffiffiffiffi Non-resonant condition Resonant condition p ð Þ e ð ffiffiffiffiffi Þ Fig. 1. Steady, bowl-shaped long wave solid line) driven by a steady, non-resonant wave group thin line) with S xx varying as indicated by. p Fig. 3. At resonance, c g = ffiffiffiffiffi gh, which happens in the shallow water limit, the Gaussian shaped S xx forcing from the wave pulse generates an И-shaped long wave which grows linearly with time.

42 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 The phase shift in the positively correlated IG wave in the inner surf zone is due to a strong interaction between short waves and IG motions in very shallow waters merging of short frequency waves) Free surface time series at different locations along the numercal wave flume Merging of high frequency waves on a bichromatic experiment Van Dongeren et al., 2007)

43 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 ModelPerformanceforIncidentandReflectedIGWaves LongWave TimeStacks LongWave Amplitude Total UnderesLmaLonof incidentigwave Incident GoodrepresentaLon ofincidentigwave generalonandshoaling Reflected UnderesLmaLonof reflectedigwave Black : Experiments Red : Model Dashed line : theoretical free long wave amplitude shoaling

44 III.INFRAGRAVITYWAVES PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 Summary Maximum run-ups under highly nonlinear waves are strongly dependent on infragravity wave motions strong under estimation of maximum run-ups using linear wave theories) Fully nonlinear Boussinesq-type equations including breaking and run-up are able to cope with the complex energy transfer processes within the nearshore producing accurate estimations of short wave propagation and IG generation and dynamics More research is needed to fully) understand nearshore wave processes and its un)expected consequences on morphodynamics and coastal hazards

45 PanQAmericanAdvancedStudiesInsLtute TheScienceofPredicLngandUnderstandingTsunamis,Storm SurgesandTidalPhenomena BostonUniversity MechanicalEngineering I.MoLvaLon PRESENTATIONOUTLINE II.NonlinearWavePropagaLonintheNearshore III.ANumericalandExperimentalStudyonInfragravityWaves IV.ChileasanInternaLonalNaturalCoastalLaboratory

46 IV.NaturalCoastalLaboratory PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 MataquitoRiverMouthintheMauleRegion Main/Wave/ direchon/////// Deep/water)/ N! DuneZone Maule/River/Mouth/ Source:Googleearth&Geoeye

47 IV.NaturalCoastalLaboratory PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 Thisareawasheavilyaffectedbythe2010Tsunami The land subsided ~ m) The sand spit was washed away by tsunami waves The sand spit rapidly reformed under highly energetic waves strong wave and aeolian alongshore sand transport) Three years of low river discharge Thesandspitsreformedbut differentthanbefore

48 IV.NaturalCoastalLaboratory PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013

49 IV.NaturalCoastalLaboratory PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013

50 IV.NaturalCoastalLaboratory PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 Video images post processed by R. Almar, IRD-LEGOS, France

51 PASICoastalHazards2013 BostonUniversity MechanicalEngineering UTFSM2Q13January2013 Acknowledgements TheFrenchconnecLonDr.E.BarthelemyandDr.H. Michallet,LEGIQGrenoble;Dr.P.Bonneton,U.Bordeaux;Dr. F.Marche,U.Montpellier;Dr.R.Almar,IRDQLEGOS) TheChileanEmergingCoastalForceDr.P.Catalan,UTFSM; Dr.c)P.Winckler,UV;Dr.C.Escauriaza,MSc.M.Guerra, MSc.J.C.Dominguez,Dr.c)L.Suarez,Dr.c)M.Villagran, J.C.Aguilera,J.Galaz,R.Campino,E.Gonzalez,B.Carrión,L. Duarte,PUC;alotofUTFSMstudents!) InsLtutoNacionaldeHidráulica FondecytprojectsNo Q andECOSQConicyt projectc07u01