Earth Rotation

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Earth Rotation

• Earths 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

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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 Earths rotation frequency, W
• W 7.29 x 10-5 s-1 (radians per sec)

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Earth Rotation

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

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Ve Decreases with Latitude

• Ve(f) W Re cos(f)

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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

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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

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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)
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Coriolis Force and Deflection of Flight Path
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• http//www.icess.ucsb.edu/davey/Geog163_S2006/cor
  iolis.mov

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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
• Its a matter of frame of reference,
  there is NO Coriolis force

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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 -gt 1 Newton 1 N 1 kg (m s-2)
• N m-2 kg m-1 s-2

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Wind Stress

• Wind stress is modeled as tw C U2
• where C 2x10-3 U is wind speed
• Values of C can vary by factor of 2

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Wind Stress

• Calculations
• If U 15 knots, what is the wind stress?
• Steps
• Convert U in knots to U in m/s
• Calculate tw

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Wind Stress

• Facts
• 1o latitude 60 nautical miles 111 km
• 15 knots 15 nautical miles / hour

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Wind Stress

• Finishing up the calculation...
• tw C U2
• (2x10-3) (7.7 m/s)2
• 0.12 N/m2
• Were done!!
• But what were the units of C?

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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
• -gt C 2x10-3 kg m-3
• Typically, C is defined as ra CD
• ra density air CD drag coefficient

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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

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Wind Stress

• Vertical eddy viscosity quantifies the air-sea
  exchanges of horizontal momentum

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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

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Vertical Eddy Viscosity

• Similar to discussion of eddy diffusion
  (turbulence mixes scalars momentum similarly)
• Values of Az (vertical) ltlt Ah (horizontal)
• Az decreases as stratification increases
• Az is at its greatest in the mixed layer

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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

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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