Transcript Importance of Photochemical Processes in the Sea

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 (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)
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)
W
Ve Decreases with Latitude
500
450
400
300
250
V
earth
(m/s)
350
200
150
Ve(f) = W Re cos(f)
100
50
0
-80
-60
-40
-20
0
20
latitude (N)
40
60
80
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
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
an object with an Coriolis
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)
Force
Coriolis Force and Deflection of Flight Path
http://www.youtube.com/watch?v=_36MiCU
S1ro
http://www.youtube.com/watch?v=49JwbrXc
Pjc
http://www.youtube.com/watch?v=KdD3Wq2
DCWQ
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, 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
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
Wind Stress
• Calculations…
If U = 15 knots, what is the wind stress?
• Steps
– Convert U in knots to U in m/s
– Calculate tw
Wind Stress
Facts:
1o latitude = 60 nautical miles = 111 km
15 knots = 15 nautical miles / hour
15knots  ...
15nmile  1hour 111x1000m 

 2


 hour 60 sec  60nmile 
7.7m/s
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?
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
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 airsea 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, tw = 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]