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OCN 5401 Chapter 5 Equations of Motion Instructor: Dr. George A. Maul gmaul@fit.edu / X 7453
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Forces affecting seawater (excluding tidal forces, etc.) Acceleration = Pressure gradient force + Coriolis force + Gravity + Friction Infrared Image of Florida Current
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Foucault Pendulum Jean Bernard Léon Foucault t in seconds; n o in degrees per sidereal day Ultimate proof (1851) that Earth rotates! BUT Aristarchus 310-230 BC thought so too!
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Gravitation and Gravity Toward Earth’s center (d Earth ≈6378 km) Earth’s rotation Ω causes two apparent forces: gravity and Coriolis outward
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Coriolis Effect http://www.youtube.com/ watch?v=mcPs_OdQOYU Gaspard-Gustave de Coriolis
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Coriolis Parameter (f) Earth rotates 2π radians in 23 h 56 m 4.1 s one sidereal day. On a rotating planet, centrifugal force is Ω 2 R, where R is the radius at that latitude. Now if a parcel moves eastward at speed U, there is an added angular velocity U/R. The new total force: 0.729x10 -4 Coriolis force
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Ocean Currents are nearly geostrophic: Coriolis balances Pressure Gradient
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Horizontal Pressure Gradient Force (per unit mass) level surface (geoid) sea surface p2p2 p1p1 ΔxΔx h2h2 h1h1 Units?
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Role of Surface Friction Fill lows and empty highs
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Austausch Coefficients also called exchange coefficient, eddy coefficient, or eddy diffusivity Compare with dynamic (molecular) viscosity for laminar flow: and A z is probably depth dependent
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Vertical Friction
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Horizontal Friction Gulf Stream cross-current model velocity shear friction
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Global Sea Surface Dynamic Topography Not the Geoid!
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Sea Surface Dynamic Topography Variability
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Oceanic Eddies Vorticity
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Relative Vorticity (ζ)
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Beta plane (beta a constant – usually over mid-latitudes)
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Absolute Vorticity (ζ A ) and Divergence (D h )
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Charleston Bump Retroflection Gulf Stream Meanders Potential Vorticity Conservation
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Approximations
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OCN 5401 Questions? Chapter 5
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