earth rotation earth’s rotation gives rise to a fictitious force called the coriolis force it...
Post on 20-Dec-2015
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TRANSCRIPT
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
• 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)
Earth Rotation
• Velocity of Earth surface
• Ve(Eq) = Re
Re = radius Earth (6371 km)
Ve(Eq) = 464 m/s
• As latitude, , increases,
Ve() will decrease
• Ve() = Re cos()
Ve Decreases with Latitude
-80 -60 -40 -20 0 20 40 60 800
50
100
150
200
250
300
350
400
450
500
latitude (N)
Vearth
(m/s)
Ve() = Re cos()
Earth Rotation
• Moving objects on Earth move with the rotating frame
(Ve()) & relative to it (vrel)
• The absolute velocity is vabs = vrel + Ve()
• 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() at that latitude will
Rotation, cont.
• Frictionless object moving north
vabs = const., but Ve() 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
Coriolis Forcean 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)
Coriolis Force and Deflection of Flight Path
http://www.youtube.com/watch?v=_36MiCUS1ro
http://www.youtube.com/watch?v=49JwbrXcPjc
http://www.youtube.com/watch?v=KdD3Wq2DCWQ
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…
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
Wind Stress
• Wind stress is modeled as w =
C U2
where C ~ 2x10-3 & U is wind speed
• Values of C can vary by factor of 2
Wind Stress
• Calculations…
If U = 15 knots, what is the wind stress?
• Steps
– Convert U in knots to U in m/s
– Calculate w
Wind Stress
Facts:
1o latitude = 60 nautical miles = 111 km
15 knots = 15 nautical miles / hour
€
15knots = ...
15nmile
hour
⎛
⎝ ⎜
⎞
⎠ ⎟1hour
602 sec
⎛
⎝ ⎜
⎞
⎠ ⎟111x1000m
60nmile
⎛
⎝ ⎜
⎞
⎠ ⎟=
7.7m/s
Wind Stress
Finishing up the calculation...
w = C U2
= (2x10-3) (7.7 m/s)2
= 0.12 N/m2
We’re done!!
But what were the units of C?
What are the units of C?
•We know that w = C U2
w =[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 a CD
a = density air & CD = drag
coefficient
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
Wind Stress
Vertical eddy viscosity quantifies the air-sea exchanges of horizontal momentum
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
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
Review
• Wind stress accounts for the input of
momentum into the ocean by the wind
• Calculated using wind speed, w = C
U2
• Processes driving wind stress &
vertical eddy viscosity are very
complex
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]