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OCN 5401 Chapter 5 Equations of Motion Instructor: Dr. George A. Maul gmaul@fit.edu / X 7453 Slide 2 Forces affecting seawater (excluding tidal forces, etc.) Acceleration = Pressure gradient force + Coriolis force + Gravity + Friction Infrared Image of Florida Current Slide 3 Foucault Pendulum Jean Bernard Lon 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! Slide 4 Gravitation and Gravity Toward Earths center (d Earth 6378 km) Earths rotation causes two apparent forces: gravity and Coriolis outward Slide 5 Coriolis Effect http://www.youtube.com/ watch?v=mcPs_OdQOYU Gaspard-Gustave de Coriolis Slide 6 Coriolis Parameter (f) Earth rotates 2 radians in 23 h 56 m 4.1 s one sidereal day. On a rotating planet, centrifugal force is 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 Slide 7 Ocean Currents are nearly geostrophic: Coriolis balances Pressure Gradient Slide 8 Horizontal Pressure Gradient Force (per unit mass) level surface (geoid) sea surface p2p2 p1p1 xx h2h2 h1h1 Units? Slide 9 Role of Surface Friction Fill lows and empty highs Slide 10 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 Slide 11 Vertical Friction Slide 12 Horizontal Friction Gulf Stream cross-current model velocity shear friction Slide 13 Global Sea Surface Dynamic Topography Not the Geoid! Slide 14 Sea Surface Dynamic Topography Variability Slide 15 Oceanic Eddies Vorticity Slide 16 Relative Vorticity () Slide 17 Beta plane (beta a constant usually over mid-latitudes) Slide 18 Absolute Vorticity ( A ) and Divergence (D h ) Slide 19 Charleston Bump Retroflection Gulf Stream Meanders Potential Vorticity Conservation Slide 20 Approximations Slide 21 OCN 5401 Questions? Chapter 5