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Earth Rotation

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. Earth Rotation.

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Earth Rotation

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  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 (2p rad/day) • Earth rotates about the sun (2p rad/365.25 day) • Relative to the “distant stars” (2p rad/86164 s) • Sidereal day = 86164 sec (Note: 24 h = 86400 sec) • Defines the Earth’s rotation frequency, W W = 7.29 x 10-5 s-1(radians per sec)

  3. W Earth Rotation • Velocity of Earth surface • Ve(Eq) = ReW Re = radius Earth (6371 km) Ve(Eq) = 464 m/s • As latitude, f, increases, Ve(f) will decrease • Ve(f) = W Re cos(f)

  4. Ve Decreases with Latitude Ve(f) = W Re cos(f)

  5. Earth Rotation • Moving objects on Earth move with the rotating frame (Ve(f)) & relative to it (vrel) • The absolute velocity is vabs = vrel + Ve(f) • Objects moving north from Equator will have a larger Ve than that under them • If “real” forces sum to 0, vabs will not change, but the Ve(f) at that latitude will

  6. Rotation, cont. • Frictionless object moving north vabs = const., but Ve(f) is decreasing vrel 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

  7. 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)

  8. Coriolis Force and Deflection of Flight Path

  9. http://www.youtube.com/watch?v=_36MiCUS1ro http://www.youtube.com/watch?v=49JwbrXcPjc http://www.youtube.com/watch?v=KdD3Wq2DCWQ

  10. 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…

  11. Wind Stress • Wind stress, tw, accounts for the input of momentum into the ocean by the wind • Exact processes creating tw is complex • tw 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

  12. Wind Stress • Wind stress is modeled astw = C U2 where C ~ 2x10-3 & U is wind speed • Values of C can vary by factor of 2

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

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

  15. Wind Stress Finishing up the calculation... tw = C U2 = (2x10-3) (7.7 m/s)2 = 0.12 N/m2 We’re done!! But what were the units of C?

  16. What are the units of C? • We know that tw = C U2 tw=[N/m2] = [kg m-1 s-2] & U2 = [(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 ra CD ra = density air & CD = drag coefficient

  17. 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

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

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

  20. Vertical Eddy Viscosity • Similar to discussion of eddy diffusion(turbulence mixes scalars & momentum similarly) • Values of Az (vertical) << Ah (horizontal) • Az decreases as stratification increases • Az is at its greatest in the mixed layer

  21. Review • Wind stress accounts for the input of momentum into the ocean by the wind • Calculated using wind speed, tw = C U2 • Processes driving wind stress & vertical eddy viscosity are very complex

  22. 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]

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