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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

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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)

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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( )

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V e Decreases with Latitude V e ( ) = R e cos( )

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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

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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

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

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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 It’s a matter of frame of reference, there is NO Coriolis force…

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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

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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

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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 w

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

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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?

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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

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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, 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

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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

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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

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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]

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