Steady State General Ocean Circulation

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Steady State General Ocean Circulation
steady state means constant in time, no
accelerations
or
Sum of all forces 0
Outline 1. Ekman dynamics (CoriolisFriction)
2. Geostrophic dynamics (CoriolisPressure
gradients) 3. EkmanGeostrophy with Coriolis
as ff0by
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The subtropical gyre circulation is a geostrophic
flow (with many eddies)
From WHP Pacific Atlas (Talley,
2007) http//www-pord.ucsd.edu/whp_atlas
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Geostrophy Coriolis balances pressure
gradient Geostrophic Degeneracy
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Ekman balance Coriolis Friction
a-1?(2Az/f) is a vertical decay scale
20m-60m
from Stewart, 2005
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Ekman velocity spiral

• Surface velocity to the right of the wind
  (northern hemisphere, due to Coriolis)
• Surface layer pushes next layer down slightly the
  right, and slightly weaker current
• Next layer pushes next layer, slightly to right
  and slightly weaker current
• Producing a spiral of the current vectors, to
  right in northern hemisphere, decreasing speed
  with increasing depth
• Details of the spiral depend on the vertical
  viscosity (how frictional the flow is, and also
  whether friction depends on depth)

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Ekman transport

• The wind stress on the ocean surface is the
  vector
• ? ( ?(x) , ?(y) )
• Integrate the Coriolis/friction balances in the
  vertical
• x -fv ?/?z(AV?u/?z) -gt -fVEK AV?u/?z
  ?(x) /?
• y fu ?/?z(AV?v/?z) -gt fUEK AV?v/?z
  ?(y) /?
• UEK and VEK are the Ekman transport ?udz, ?vdz
• Ekman transport is exactly to the right of the
  wind stress (northern hemisphere ).
• Ekman transport does not depend on the size or
  structure of AV (but the detailed structure of
  the spiral DOES depend on it)

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Ekman layer transport

• Transport 90 to wind, to right in northern
  hemisphere
• UEk ?/?f (units are m2/s, not m3/s so
  technically this is not a transport need to sum
  horizontally along a section to get a transport).
• Typical size for wind stress 0.1 N/m2, UEk 1
  m2/s. Integrate over width of ocean, say 5000 km,
  get total transport of 5 x 106 m3/sec 5 Sv.

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Ekman layer depth

• Depth depends on eddy viscosity AV (why?)
  Dek (2AV/f)1/2
• Eddy viscosity is about 0.05 m2/sec in turbulent
  surface layer, so Ekman layer depth is 20 to 60 m
  for latitudes 80 to 10.

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Ekman layer velocity

• Velocity spirals with depths and magnitude
  depends on eddy viscosity. If AV is constant,
  surface velocity is 45 to wind
• For eddy viscosity 0.05 m2/sec, and wind stress
  of 1 dyne/cm2 (.1 N/m2), surface velocity is 3
  cm/sec at 45N.

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Observations of Ekman layer
Direct current measurements in California Current
region revealed excellent Ekman-type spiral
(Chereskin, JGR, 1995)
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Global surface wind velocity
Westward Eastward
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Ekman divergence (Ekman upwelling) at equator and
at land boundaries

• Equatorial Land boundary
• (southern hemisphere, like Peru)
  

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Ekman transport convergence and divergence
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Ekman transport convergence and divergence
Ekman Pumping
Geostrophic flow
Vertical velocity at base of Ekman layer order
(10-4cm/sec) (Compare with typical horizontal
velocities of 1-10 cm/sec)
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Pacific winds (mean)

• Ekman pumping
• Gray downwelling
• White upwelling

from Talley 2006
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Ekman Pumping
continuity
vertical integral
Ekman transports
Convergence in Ekman transport
Vertical velocity Ekman pumping
Recall MEx ?y/rf Ekman transport 90 degrees
to wind MEy -tx/rf