1. Earth Rotation Earth’s rotation gives rise to a fictitious force called the Coriolis force It accounts for the apparent deflection of motions viewed in our rotating frame Analogies –throwing a ball from a merry-go-round –sending a ball to the sun

2. Earth Rotation Earth rotates about its axis wrt sun (2  rad/day) Earth rotates about the sun (2  rad/365.25 day) Relative to the “distant stars” (2  rad/86164 s) –Sidereal day = 86164 sec (Note: 24 h = 86400 sec) Defines the Earth’s rotation frequency,   = 7.29 x 10 -5 s -1 (radians per sec)

3. Earth Rotation Velocity of Earth surface V e (Eq) = R e  R e = radius Earth (6371 km) V e (Eq) = 464 m/s As latitude, , increases, V e (  ) will decrease V e (  ) =  R e cos(  ) 

4. V e Decreases with Latitude V e (  ) =  R e cos(  )

6. Earth Rotation Moving objects on Earth move with the rotating frame (V e (  )) & relative to it (v rel ) The absolute velocity is v abs = v rel + V e (  ) Objects moving north from Equator will have a larger V e than that under them If “real” forces sum to 0, v abs will not change, but the V e (  ) at that latitude will

7. Rotation, cont. Frictionless object moving north v abs = const., but V e (  ) is decreasing v rel must increase (pushing the object east) When viewed in the rotating frame, moving objects appear deflected to right (left SH) Coriolis force accounts for this by proving a “force” acting to the right of motion

8. Coriolis Force an object with an initial east-west velocity will maintain that velocity, even as it passes over surfaces with different velocities. As a result, it appears to be deflected over that surface (right in NH, left in SH)

9. Coriolis Force and Deflection of Flight Path

11. http://www.youtube.com/watch?v=_36MiCU S1ro http://www.youtube.com/watch?v=49JwbrXc Pjc http://www.youtube.com/watch?v=KdD3Wq2 DCWQ

12. Earth Rotation Motions in a rotating frame will appear to deflect to the right (NH) Deflection will be to the right in the northern hemisphere & to left in southern hemisphere No apparent deflection right on the equator It’s a matter of frame of reference, there is NO Coriolis force…

13. Wind Stress Wind stress,  w, accounts for the input of momentum into the ocean by the wind Exact processes creating  w is complex  w is a tangential force per unit area Units are Newton (force) pre meter squared F = ma -> 1 Newton = 1 N = 1 kg (m s -2 ) N m -2 = kg m -1 s -2

14. Wind Stress Wind stress is modeled as  w = C U 2 where C ~ 2x10 -3 & U is wind speed Values of C can vary by factor of 2

15. Wind Stress Calculations… If U = 15 knots, what is the wind stress? Steps – Convert U in knots to U in m/s – Calculate  w

16. Wind Stress Facts: 1 o latitude = 60 nautical miles = 111 km 15 knots = 15 nautical miles / hour

17. Wind Stress Finishing up the calculation...  w = C U 2 = (2x10-3) (7.7 m/s) 2 = 0.12 N/m 2 We’re done!! But what were the units of C?

18. What are the units of C? We know that  w = C U 2  w =[N/m 2 ] = [kg m -1 s -2 ] & U 2 = [(m/s) 2 ] C = [kg m -1 s -2 ] / [m 2 s -2 ] = [kg m -3 ] -> C ~ 2x10 -3 kg m -3 Typically, C is defined as  a C D  a = density air & C D = drag coefficient

19. Wind Stress Many processes contribute to transfer of momentum from wind to the ocean – Turbulent friction – Generation of wind waves – Generation of capillary waves Key is the recognition that the process is turbulent

20. Wind Stress Vertical eddy viscosity quantifies the air- sea exchanges of horizontal momentum

21. Vertical Eddy Viscosity Vertical eddy viscosity, A z, controls the efficiency of wind momentum inputs High values of A z suggest deeper penetration of momentum into the ocean Values of A z are functions of – turbulence levels – wave state – stratification near the surface

22. Vertical Eddy Viscosity Similar to discussion of eddy diffusion (turbulence mixes scalars & momentum similarly) –Values of A z (vertical) << A h (horizontal) –A z decreases as stratification increases –A z is at its greatest in the mixed layer

23. Review Wind stress accounts for the input of momentum into the ocean by the wind Calculated using wind speed,  w = C U 2 Processes driving wind stress & vertical eddy viscosity are very complex

24. Ekman Transport Ekman transport is the direct wind driven transport of seawater Boundary layer process Steady balance among the wind stress, vertical eddy viscosity & Coriolis forces Story starts with Fridtjof Nansen [1898]