The Mathematics of Marine Modelling: Water, Solute and Particle Dynamics in Estuaries and Shallow Seas PDF
Preview The Mathematics of Marine Modelling: Water, Solute and Particle Dynamics in Estuaries and Shallow Seas
Mathematics of Planet Earth 9 Henk Schuttelaars Arnold Heemink Eric Deleersnijder Editors The Mathematics of Marine Modelling Water, Solute and Particle Dynamics in Estuaries and Shallow Seas Mathematics of Planet Earth Volume 9 SeriesEditors DanCrisan,ImperialCollegeLondon,London,UK KenGolden,UniversityofUtah,SaltLakeCity,UT,USA DarrylD.Holm,ImperialCollegeLondon,London,UK MarkLewis,UniversityofAlberta,Edmonton,AB,Canada YasumasaNishiura,TohokuUniversity,Sendai,Miyagi,Japan JosephTribbia,NationalCenterforAtmosphericResearch,Boulder,CO,USA JorgePassamaniZubelli,InstitutodeMatemáticaPuraeAplicada,RiodeJaneiro, Brazil Thisseriesprovidesavarietyofwell-writtenbooksofavarietyoflevelsandstyles, highlightingthefundamentalroleplayedbymathematicsinahugerangeofplanetary contexts on a global scale. Climate, ecology, sustainability, public health, diseases andepidemics,managementofresourcesandriskanalysisareimportantelements. Themathematicalsciencesplayakeyroleintheseandmanyotherprocessesrelevant toPlanetEarth,bothasafundamentaldisciplineandasakeycomponentofcross- disciplinaryresearch.Thiscreatestheneed,bothineducationandresearch,forbooks thatareintroductorytoandabreastofthesedevelopments. Springer’s MoPE series will provide a variety of such books, including mono- graphs,textbooks,contributedvolumesandbriefssuitableforusersofmathematics, mathematiciansdoingresearchinrelatedapplications,andstudentsinterestedinhow mathematicsinteractswiththeworldaroundus.Theserieswelcomessubmissions on any topic of current relevance to the international Mathematics of Planet Earth effort,andparticularlyencouragessurveys,tutorialsandshortercommunicationsin alivelytutorialstyle,offeringaclearexpositionofbroadappeal. ResponsibleEditors: MartinPeters,Heidelberg([email protected]) RobinsondosSantos,SãoPaulo([email protected]) AdditionalEditorialContacts: DonnaChernyk,NewYork([email protected]) MasayukiNakamura,Tokyo([email protected]) · · Henk Schuttelaars Arnold Heemink Eric Deleersnijder Editors The Mathematics of Marine Modelling Water, Solute and Particle Dynamics in Estuaries and Shallow Seas Editors HenkSchuttelaars ArnoldHeemink DepartmentofAppliedMathematics DepartmentofAppliedMathematics DelftUniversityofTechnology DelftUniversityofTechnology Delft,TheNetherlands Delft,TheNetherlands EricDeleersnijder InstituteofMechanics,MaterialsandCivil Engineering(IMMC)andEarthandLife Institute(ELI) UniversitéCatholiquedeLouvain Louvain-la-Neuve,Belgium ISSN 2524-4264 ISSN 2524-4272 (electronic) MathematicsofPlanetEarth ISBN 978-3-031-09558-0 ISBN 978-3-031-09559-7 (eBook) https://doi.org/10.1007/978-3-031-09559-7 ©SpringerNatureSwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Coastalregionsarestronglyimpactedbyhumaninterventionsandclimatechange. Sealevelriseandincreasedstorminessthreatencoastalsafety;changesinintensity and duration of rainfall strongly impact intrusion of salt which may endanger the availabilityoffreshwater.Examplesofhumaninterventionsarethemeasurestomiti- gatetheseadverseclimateeffects,butalsointerventionsaredrivenby,forexample, economic (e.g., deepening of shipping channels, sand mining) and environmental (e.g.,constructionoflarge-scalewindparks)reasons.Unfortunately,suchinterven- tionsmayhaveunintendednegativeimpactsduetothemanyconflictinginterestsin theseregions:forexample,channeldeepeningmaybeanexcellentchoicefroman economicpointofview,butitmayresultinadeteriorationofthecoastalsafetyand ecological values of the system under consideration. To oversee the multi-faceted impactofinterventionsandclimatechange,thedynamicsofcoastalseas,estuaries, andtidalinletshavetobewell-understood.Onlywithsuchunderstanding,coastal managerscanmakewell-balanceddecisionsthattakeallaspectsintoaccount.Math- ematicalmodelingofmarinesystemsbecomesincreasinglyimportanttoprovidethe insightsnecessaryfordecisionmaking. Overthepastfewdecades,themathematicalmodelingcyclehasbecomeinstru- mental in understanding the dynamics of coastal seas, estuaries, and tidal inlet systems.Inthiscycle,newmathematicalmodelsaredevelopedorexistingmodels are improved upon, advanced solution techniques are developed and employed to solvethesehighlycomplexnonlinearmodels,andthemodeloutcomesareanalyzed using state-of-the-art mathematical techniques and, if possible, compared to field andlaboratoryobservations. In this contribution, we focus on mathematical techniques available to study varioustopicsfrommarinesciencesinestuariesandcoastalseas.Sinceonlyalimited number of topics can be treated, we restrict ourselves to the discussion of mathe- matical models on water motion and transport of pollutants and sediments by the water motion. In the first chapter, the basic mathematical concepts to obtain the governingequationsaresummarizedandthefinalsystemofequationstomodelthe watermotionincoastalregionsisgiven.Inthenextchapters,specificaspectsofwater motionarediscussed:waterwavesinisotropicandanisotropicmedia,(near-shore) v vi Preface waves,andbarotropictides.Thisisfollowedbyadetailedreviewof2D-turbulence modeling and parameterization of turbulent dispersion. In the final chapters, river plumes, mathematical techniques to model transport phenomena, morphodynamic modelingofthebathymetryandgeometry,andaccuratelymodeldryingandflooding arediscussed. Theprerequisitemathematicalknowledgevaries,butmostofthematerialshould be accessible to advanced graduate students and early-stage researchers. In most chapters, there is a clear link with observations and practical challenges, allowing professionals outside academia and decision-makers to get a good insight into the various techniques underpinning the models often used and other methodologies thatcan be employed to tackle their real-world problems. Ineach chapter, there is anextensivelistofreferences,rangingfromgeneraltohighlyspecialized,allowing theinterestedreadertofurtherexplorethesetopicsindependently. Delft,TheNetherlands EricDeleersnijder February,2022 ArnoldHeemink HenkSchuttelaars Contents 1 BasicEquationsofMarineFlows ............................... 1 KnutKlingbeil,EricDeleersnijder,OliverFringer,andLarsUmlauf 2 Water Waves in Isotropic and Anisotropic Media: Acomparison ................................................. 11 LeoR.M.Maas 3 AReviewofNonlinearBoussinesq-TypeModelsforCoastal OceanModeling .............................................. 45 ClintDawsonandAliSamii 4 TidesinCoastalSeas.InfluenceofTopographyandBottom Friction ...................................................... 73 PieterC.RoosandHuibE.deSwart 5 Variational Water-Wave Modeling: From Deep Water toBeaches .................................................... 103 OnnoBokhove 6 Quasi-2DTurbulenceinShallowFluidLayers ................... 135 HermanJ.H.Clercx 7 TurbulentDispersion .......................................... 167 BenoitCushman-Roisin 8 SpreadingandMixinginNear-FieldRiverPlumes ............... 197 RobertD.Hetland 9 Lagrangian Modelling of Transport Phenomena Using StochasticDifferentialEquations ............................... 213 ArnoldHeemink, EricDeleersnijder, SyedHyderAliMuttaqiShah,andUlfGräwe vii viii Contents 10 MorphodynamicModellinginMarineEnvironments:Model FormulationandSolutionTechniques ........................... 243 H.M.SchuttelaarsandT.J.Zitman 11 WettingandDryingProceduresforShallowWaterSimulations .... 287 SigrunOrtleb,JonathanLambrechts,andTuomasKärnä Index ............................................................. 315 Contributors BokhoveOnno SchoolofMathematics,UniversityofLeeds,LS29JT,Leeds,UK ClercxHermanJ.H. FluidDynamicsLaboratory,DepartmentofAppliedPhysics, EindhovenUniversityofTechnology,Eindhoven,MB,TheNetherlands Cushman-RoisinBenoit Thayer School of Engineering, Dartmouth College, Hanover,NewHampshire,USA DawsonClint Oden Institute for Computational Engineering and Sciences, The UniversityofTexasatAustin,Austin,TX,USA DeleersnijderEric Université Catholique de Louvain, Ottignies-Louvain-la- Neuve,Belgium deSwartHuibE. Institute for Marine and Atmospheric research, Department of Physics,UtrechtUniversity,Utrecht,TheNetherlands FringerOliver StanfordUniversity,Stanford,CA,USA GräweUlf LeibnizInstituteforBalticSeaResearchWarnemünde(IOW),Rostock, Germany HeeminkArnold DelftUniversityofTechnology,Delft,Netherlands HetlandRobertD. DepartmentofOceanography,TexasA&MUniversity,College Station,CollegeStation,TX,USA KärnäTuomas FinnishMeteorologicalInstitute,Helsinki,Finland KlingbeilKnut Leibniz Institute for Baltic Sea Research Warnemünde (IOW), Rostock,Germany LambrechtsJonathan Institute of Mechanics, Materials and Civil Engineering, UniversitécatholiquedeLouvain,Louvain-la-Neuve,Belgium MaasLeoR.M. InstituteforMarineandAtmosphericResearch(IMAU),Utrecht University,Utrecht,Netherlands ix
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