1. OCN 5401 Chapter 5 Equations of Motion Instructor: Dr. George A. Maul gmaul@fit.edu / X 7453

2. Forces affecting seawater (excluding tidal forces, etc.) Acceleration = Pressure gradient force + Coriolis force + Gravity + Friction Infrared Image of Florida Current

3. 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!

4. Gravitation and Gravity Toward Earth’s center (d Earth ≈6378 km) Earth’s rotation Ω causes two apparent forces: gravity and Coriolis outward

5. Coriolis Effect http://www.youtube.com/ watch?v=mcPs_OdQOYU Gaspard-Gustave de Coriolis

6. 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

7. Ocean Currents are nearly geostrophic: Coriolis balances Pressure Gradient

8. Horizontal Pressure Gradient Force (per unit mass) level surface (geoid) sea surface p2p2 p1p1 ΔxΔx h2h2 h1h1 Units?

9. Role of Surface Friction Fill lows and empty highs

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

11. Vertical Friction

12. Horizontal Friction Gulf Stream cross-current model velocity shear friction

13. Global Sea Surface Dynamic Topography Not the Geoid!

14. Sea Surface Dynamic Topography Variability

15. Oceanic Eddies Vorticity

16. Relative Vorticity (ζ)

17. Beta plane (beta a constant – usually over mid-latitudes)

18. Absolute Vorticity (ζ A ) and Divergence (D h )

19. Charleston Bump Retroflection Gulf Stream Meanders Potential Vorticity Conservation

20. Approximations

21. OCN 5401 Questions? Chapter 5