Nonlinear Internal Waves in Lakes PDF
Preview Nonlinear Internal Waves in Lakes
Advances in Geophysical and Environmental Mechanics and Mathematics Series Editor: Professor Kolumban Hutter For furthervolumes: http://www.springer.com/series/7540 Board of Editors Aeolean Transport, Sediment Transport, Granular Flow Prof.HansHerrmann Institutfu¨rBaustoffe DepartementBau,UmweltundGeomatik HIFE12/ETHHo¨nggerberg 8093Zu¨rich,Switzerland [email protected] Avalanches, Landslides, Debris Flows, Pyroclastic Flows, Volcanology ProfE.BrucePitman DepartmentofMathematics UniversityofBuffalo Buffalo,N.Y.14260,USA [email protected] Hydrological Sciences Prof.VijayP.Singh WaterResourcesProgram DepartmentofCivilandEnvironmentalEngineering LouisianaStateUniversity BatonRouge,LA70803-6405,USA Nonlinear Geophysics Prof.EfimPelinovsky InstituteofAppliedPhysics 46UljanovStreet 603950NizhniNovgorod,Russia [email protected] Planetology, Outer Space Mechanics ProfHeikkiSalo DivisionofAstronomy DepartmentofPhysicalSciences UniversityofOulu 90570Oulu,Finnland Glaciology, Ice Sheet and Ice Shelf Dynamics, Planetary Ices Prof.Dr.RalfGreve InstituteofLowTemperatureScience HokkaidoUniversity Kita-19,Nishi-8,Kita-ku Sapporo060-0819,Japan [email protected] http://wwwice.lowtem.hokudai.ac.jp/(cid:1)greve/ Kolumban Hutter Editor Nonlinear Internal Waves in Lakes Editor Prof.Dr.KolumbanHutter ETHZu¨rich c/oVersuchsanstaltfu¨rWasserbau HydrologieundGlaziologie Gloriastr.37/39 8092Zu¨rich Switzerland [email protected] ISSN1866-8348 e-ISSN1866-8356 ISBN978-3-642-23437-8 e-ISBN978-3-642-23438-5 DOI10.1007/978-3-642-23438-5 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2011942325 #Springer-VerlagBerlinHeidelberg2012 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnot imply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotec- tivelawsandregulationsandthereforefreeforgeneraluse. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface INTAS has been an international association for the promotion of collaboration between scientists from the European Union, Island, Norway, and Switzerland (INTAScountries)andscientistsfromthenewindependentcountriesoftheformer SovietUnion(NUScountries).Theprogramwasfoundedin1993,existeduntil31 December 2006 and is since 01 January 2007 in liquidation. Its goal was the furthering of multilateral partnerships between research units, universities, and industries in the NUS and the INTAS membercountries. In the year 2003, on the suggestionofDr.V.Vlasenko,thewriterinitiatedaresearchprojecton“Strongly nonlinear internal waves in lakes: generation, transformation and meromixis” (Ref.Nr.INTAS033-51-3728)withthefollowingpartners: INTAS Prof. K. Hutter, PhD, Department of Mechanics, Darmstadt University of Technology,Darmstadt,Germany Dr. V. Vlasenko, Institute of Marine Studies, Plymouth University, Plymouth, UnitedKingdom Prof.Dr.E.Pelinovsky,InstituteofAppliedPhysics,LaboratoryofHydrophysics, Russia,AcademyofSciences,NizhniNovgorod,Russia Prof.Dr.N.Filatov,NorthernWaterProblemsInstitute,KarelianScientificCentre, RussianAcademyofSciences,Petrozavodsk,Russia Prof.Dr.V.Maderich,InstituteofMathematicalMachinesandSystemModeling, UkrainianAcademyofSciences,Kiev,Ukraine Prof.Dr.V.Nikishov,InstituteofHydrodynamics,DepartmentofVortexMotion, UkrainianAcademyofSciences,Kiev,Ukraine The joint proposal was granted with commencement on 01 March 2004 and it lasteduntil28February2007.Thewriterwasresearchandmanagementcoordina- tor;annualreportsweresubmitted. Thefinalreport,listingtheadministrativeandscientificactivities,submittedto the INTAS authorities quickly passed their scrutiny;however, it was nevertheless decidedtocollecttheachievedresultsinabookandtoextendandcomplementthe v vi Preface results obtained at that time with additional findings obtained during the 4 years after termination of the INTAS project. Publication in the Springer Verlag series “Advances in Geophysical and Environmental Mechanics and Mathematics” was arranged.ThewriterservedasEditorofthebook,nowentitled“NonlinearInternal WavesinLakes”forbrevity.Thecontributionsofthesixpartnersmentionedabove werecollectedintofourchapters.Unfortunately,eventhoughafullchapteronthe theoriesofweaklynonlinearwaveswasplanned,ProfessorE.Pelinovsky,aworld- renowned expert in this topic, withdrew his early participation. The remaining chapters contain elements of it, and the referenced literature makes an attempt of partialcompensation.StronglynonlinearwavesareadequatelycoveredinChap.4. Writingoftheindividualchapterswasprimarilydonebythefourremaininggroups; all chapters were thoroughly reviewed and criticized professionally and linguisti- cally,sometimeswithseveraliterations.Wehopethetextisnowacceptable. Internal waves and oscillations (seiches) in lakes are important ingredients of lake hydrodynamics. A large and detailed treatise on “Physics of Lakes” has recentlybeenpublishedbyHutteretal.[1,2].Itssecondvolumewiththesubtitle “LakesasOscillators”dealswithlinearwavemotionsinhomogeneousandstrati- fiedwaters,butonlylittleregardingnonlinearwavesistreatedinthesebooks.The presentbookon“NonlinearInternalWavesinLakes”canwellserveasacomple- mentarybookofthistreatiseontopicswhichwereputasidein[1,2]. Indeed, internal wave dynamics in lakes (and oceans) is an important physical componentofgeophysicalfluidmechanicsof‘quiescent’waterbodiesoftheglobe. Theformationofinternalwavesrequiresseasonalstratificationofthewaterbodies and generation by (primarily) wind forces. Because they propagate in basins of variabledepth,ageneratedwavefieldoftenexperiencestransformationfromlarge basin-wide scales to smaller scales. As long as this fission is hydrodynamically stable, nothing dramatic will happen. However, if vertical density gradients and shearing of the horizontal currents in the metalimnion combine to a Richardson numbersufficientlysmall(<¼),thelightepilimnionwatermixeswiththewaterof the hypolimnion, giving rise to vertical diffusion of substances into lower depths. This meromixis is chiefly responsible for the ventilation of the deeper waters and thehomogenizationofthewaterthroughthelakedepth.Theseprocessesaremainly formedbecauseofthephysicalconditions,buttheyplaybiologicallyanimportant roleinthetrophicationalstateofthelake. l Chapter1onInternalwavesinlakes:Generation,transformation,meromixis– an attempt of a historical perspective gives a brief overview of the subjects treatedinChaps.2–4.Sincebriefabstractsareprovidedatthebeginningofeach chapter,werestrictourselvesheretostateonlyslightlymorethantheheadings. l Chapter2isanalmanacofFieldstudiesofnonlinearinternalwavesinlakeson theGlobe.Anup-to-datecollectionofnonlinearinternaldynamicsisgivenfrom aviewpointoffieldobservation. l Chapter3presentsexclusivelyLaboratorymodelingoftransformationoflarge- amplitude internal waves by topographic obstructions. Clearly defined driving mechanismsareusedasinputsothatresponsesarewellidentifiable. Preface vii l Chapter4presentsNumericalsimulationsofthenon-hydrostatictransformation ofbasin-scaleinternalgravitywavesandwave-enhancedmeromixisinlakes.It rounds off the process from generation over transformation to meromixis and providesanexplanationofthelatter. As coordinatingauthorandeditor ofthis volume ofAGEM2, thewriter thanks all authors of the individual chapters for their patience in co-operating in the process ofvariousiterations ofthedraftedmanuscript.Hebelievesthatarespect- ablebookhasbeengenerated;letushopethatsaleswillcorroboratethis. ItisourwishtothankSpringerVerlagingeneralandDr.ChrisBendallandMrs. Agata Oelschla¨ger, in particular, for their efforts to cope with us and to do everything possible in the production stage of this book, which made this last iterationeasy. Finally, the authors acknowledge the support of their home institutions and extend their thanks to the INTAS authorities during the 3 years (2004–2007) of supportthroughINTASGrant3-51-3728. Forallauthors, Zurich,Switzerland K.Hutter References 1.Hutter,K,Wang,Y,ChubarenkoI.:PhysicsofLakes,Volume1:FoundationoftheMathemati- calandPhysicalBackground,SpringerVerlag,Berlin,etc.2011. 2.Hutter,K,Wang,Y,ChubarenkoI.:PhysicsofLakes,Volume2:LakesasOscillators,Springer Verlag,Berlin,etc.2011. . Contents 1 InternalWavesinLakes:Generation,Transformation,Meromixis– AnAttemptataHistoricalPerspective .................................. 1 K.Hutter 1.1 Thermometry ............................................................ 1 1.2 InternalOscillatoryResponses ......................................... 3 1.3 ObservationsofNonlinearInternalWaves ............................ 10 References .................................................................. 15 2 FieldStudiesofNon-LinearInternalWavesinLakesontheGlobe .. 23 N.Filatov,A.Terzevik,R.Zdorovennov,V.Vlasenko,N.Stashchuk, andK.Hutter 2.1 OverviewofInternalWaveInvestigationsinLakesontheGlobe ... 24 2.1.1 Introduction ..................................................... 24 2.1.2 ExamplesofNonlinearInternalWavesonRelatively SmallLakes ..................................................... 29 2.1.3 ExamplesofNonlinearInternalWavesinMedium- andLarge-SizeLakes ........................................... 33 2.1.4 ExamplesofNonlinearInternalWavesinGreatLakes: LakesMichiganandOntario,Baikal,LadogaandOnego ..... 41 2.1.5 SomeRemarksontheOverviewofNonlinearInternal WaveInvestigationsinLakes .................................. 49 2.2 OverviewofMethodsofFieldObservationsandDataAnalysis ofInternalWaves ...................................................... 50 2.2.1 TouchProbingMeasuringTechniques ......................... 50 2.2.2 Remote-SensingTechniques ................................... 54 2.2.3 DataAnalysisofTimeSeriesofObservationsofInternal Waves ........................................................... 60 2.3 LakeOnegoFieldCampaigns2004/2005:AnInvestigation ofNonlinearInternalWaves .......................................... 67 ix x Contents 2.3.1 FieldMeasurements ............................................ 67 2.3.2 DataAnalysis ................................................... 71 2.3.3 SummaryoftheLakeOnegoExperiments ..................... 88 2.4 ComparisonofFieldObservationsandModellingofNonlinear InternalWavesinLakeOnego ........................................ 90 2.4.1 Introduction ..................................................... 90 2.4.2 DataofFieldMeasurementsinLakeOnego ................... 91 2.4.3 Model ........................................................... 93 2.4.4 ResultsofModelling ............................................ 94 2.4.5 DiscussionandConclusions .................................... 98 References .................................................................. 99 3 LaboratoryModelingonTransformationofLarge-Amplitude InternalWavesbyTopographicObstructions ......................... 105 N.Gorogedtska,V.Nikishov,andK.Hutter 3.1 GenerationandPropagationofInternalSolitaryWavesin LaboratoryTanks ..................................................... 105 3.1.1 Introduction .................................................... 105 3.1.2 DissipationNotinFocus ...................................... 107 3.1.3 InfluenceofDissipation ....................................... 115 3.1.4 Summary ....................................................... 119 3.2 Transmission,Reflection,andFissionofInternalWavesby UnderwaterObstacles ................................................ 120 3.2.1 TransformationandBreakingofWavesbyObstaclesof DifferentHeight ............................................... 120 3.2.2 InfluenceoftheObstacleLengthonInternalSolitaryWaves 141 3.3 InternalWaveTransformationCausedbyLateralConstrictions .... 148 3.4 LaboratoryStudyoftheDynamicsofInternalWavesonaSlope ... 163 3.4.1 ReflectionandBreakingofInternalSolitaryWavesfrom UniformSlopesatDifferentAngles ........................... 163 3.4.2 InfluenceofSlopeNonuniformityontheReflectionand BreakingofWaves ............................................ 179 3.5 Conclusions ........................................................... 186 References ................................................................. 189 4 NumericalSimulationsoftheNonhydrostaticTransformationof Basin-ScaleInternalGravityWavesandWave-EnhancedMeromixis inLakes ................................................................... 193 V.Maderich,I.Brovchenko,K.Terletska,andK.Hutter 4.1 Introduction ........................................................... 193 4.1.1 PhysicalProcessesControllingtheTransferofEnergyWithin anInternalWaveFieldfromLargetoSmallScales .......... 193 4.1.2 NonhydrostaticModeling ...................................... 194 4.2 DescriptionoftheNonhydrostaticModel ............................ 196 4.2.1 ModelEquations ............................................... 196
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