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Coastal Ocean Dynamics: First Course in Hydrodynamics

Learn the basic principles of mechanics and thermodynamics in the context of coastal ocean dynamics, including conservation laws, fluid properties, Ekman dynamics, and more. Dive into the dynamic equations and geostrophic balance in this comprehensive introductory course.

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Coastal Ocean Dynamics: First Course in Hydrodynamics

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  1. Coastal Ocean Dynamics First course: Hydrodynamics Hans Burchard Leibniz Institute for Baltic Sea Research Warnemünde hans.burchard@io-warnemuende.de

  2. Whatmakesitmove? Someprinciplelawsofmechanicsandthermodynamics.

  3. Variousconservationlawsaredefined on a material volume of a homogeneoussubstance such aswaterorair, moving withtheflow.

  4. Conservationofmass Within a material body, massisconserved, i.e., thenumberofmoleculesandtheirmassremainthe same.

  5. Conservationofmomentum Momentum: density X velocity Newton‘sSecond Law: Within a material body, thechangeofmomentum isequaltosumoftheforcesacting on thebody F maybe due to a bodyforce (typicallygravitationalforce) or due to a force on thesurfaceofthebody.

  6. Conservationof angular momentum Within a material body, thechangeof total angular momentum M isequaltosumofthetorqueoftheforces acting on thebody.

  7. Actio = Reactio Newton‘s Third Law: If a body A excerts a force on a secondbody B, then B excertsthe same force on A but withthe different sign.

  8. Law ofgravitation The body B1 has mass m1, and a second body, B2 has mass m2, and they have the distance r along the unit vector, n, connecting the two. Then, the gravity force, G, between the two bodies given by where g is the universal constant of gravity.

  9. First lawofthermodynamics Balance ofenergy The changeof total energyof a material bodyisequaltotherate ofworkdonebythemechanicalforcesacting on thebody (PV) anditssurface (PA), theinternalheatsupply(R) andthe total heatflux Q throughtheboundary: 4 waystoincreasetheenergy of an apple …

  10. Second lawofthermodynamics Entropy* cannotdecreaseexceptforexternalforcing. This meansforexample … … Heat always flows from high to low temperature. … Mechanical energy can be converted into heat via friction, but not the other way around. *Measure for disorder

  11. Material laws FluidslikewaterorairarecalledNewtonian because the viscous stresses that arise from its flow, are proportional to the local shear rate.

  12. Incompressibilityconstraint In contrasttoair, waterisrelativelyincompressible. This hastheconsequencethathorizontallyconvergingwatertransportsleadto an increasingsealevel.

  13. Hydrostaticassumption If all flowisatrest, thepressure p is in hydrostaticequilibrium, i.e. theverticalpressuregradientis proportional tothedensityofthewater (gravitationalacceleration g is theconstantofproportionality): In oceanmodelsweassumethatthepressureishydrostatic also whentheflowis not atrest.

  14. Dynamic shallowwaterequations Finally, thedynamicequationsareofthefollowing form: x,y,z: westward, northwardandupwardcoordinate(m/s) u,v,w: westward, northwardandupwardvelocitycomponent (m/s) t: time (s) p: pressure (N/m2=kg/(s2m) f: Coriolis parameter (2w sin(f), f latitude, w Earth rotation rate) g: gravitationalacceleration (=9.81 m/s2) r0: referencedensity Fx,Fy: frictionterms pressure gradient rotation acceleration advection friction

  15. Decompositionofpressuregradient The pressuregradientcanbedecomposedtothreecontributions: pressuresurfacedensityatmospheric = + + pressure gradientslopegradientgradient

  16. Equationofstate Densityofseawateris a nonlinearfunctionof temperature, salinity S, pressure p: maximum density temperature freezing temperature

  17. Letusnowstudyidealisedsituationswheretwoterms in thedynamicequationsbalanceandtheothersarezero.

  18. Channel flow Balance betweenpressuregradientandfriction*. Solution forconstanteddyviscosity: Solution forparaboliceddyviscosity: *Weneedtomakehere a littleexcursionintothedefinitionofeddyviscosity

  19. Channel flow

  20. Inertialoscillations Balance between rate ofchangeand Coriolis rotation:

  21. Inertialoscillation (observations in the Western Baltic Sea) Van der Lee and Umlauf (2011)

  22. Geostrophicequilibrium Balance betweenpressuregradientand Coriolis rotation: Flow is 90° totherightofthepressuregradient.

  23. Geostrophicequilibrium Air flowaround a low-pressureareais anti-clockwise in the Northern hemisphere, andclockwise in the Southern hemishere (=cyclonic).

  24. Ekmandynamics Balance between Coriolis rotationandfriction: Verticallyintegratedtransport (U,V) is 90° totherightofthe wind stress (in Northern hemispere). This is also calledtheEkmantransport.

  25. Ekmandynamics Ekman spiral forconstanteddyviscosity: Ekmandepth: Kunduand Cohen (2002)

  26. Upwelling Ifthereis a coasttotheleft (Northern hemisphere) ofthecurrent, thentheEkmantransportiscompensatedbyupwellingwaterfromdepth: Downwellingresultsfrom a coast totherightofthe wind. upwelling Wind downwelling

  27. Kelvin waves Kelvin wavesarelongpropagatingwaveswhichlean on a coasttotheright (Northern hemisphere): Gill (1982)

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