Topic 3: surface ocean circulation

D. Ekman Transport

1. In 1890, a Norwegian oceanographer Fridtjof Nansen attempted a trip to the North Pole by freezing a ship called the Fram into the ice and letting the ship travel with the ice for three years. They reached 86ºN. (Fig. 2)

-Since ~90% of the iceberg is below the surface, the direction of iceberg flow depends on the direction of the surface current flow.

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  the Coriolis Force acts, as soon as the surface water starts to move, at a right angle to the direction of the current (to the right in the Northern Hemisphere and left in the Southern Hemisphere)
  
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  a Frictional Force acts, as soon as the water starts to move, in the opposite direction to the direction of the current flow
  
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  a Resulting Force is the force vector that results from the combined effects of the Coriolis Force and Frictional Force
  
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  as the surface current speeds up (accelerates) both Frictional Force and Coriolis Force increase and thus the Resulting Force vector increases
  

6. In response to a wind stress force, the current speed begins to increase and the current is deflected from the wind direction by the Coriolis Force, until the Resulting Force is equal in magnitude and opposite in direction to the Wind Stress Force

- at this point in time, there is a force balance

- when a force balance exists, the surface current no longer accelerates (remains at a constant speed) and remains at a fixed angle of deflection relative to the Wind Stress Force vector

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  Note: the current itself is not a force.
  
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  There are only three forces in this force balance: Wind Stress Force, Frictional Force and Coriolis Force.
  
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  The Resulting Force represents the combined force effect of the Coriolis Force and Frictional Force and exactly opposes Wind Stress force at a force balance
  

8. The deflection angle at which the surface current flows, relative to the wind direction, depends on the magnitude of the Coriolis Force.

-if the magnitude of the Coriolis Force was equal to the magnitude of the Fractional Force, then the current would flow at a 45 º angle to the wind
9. Class Problem: Draw the Force Balance for the Ekman layer in the Southern Hemisphere using a force vector picture like that shown in Fig. 5
10. The Ekman Layer and Ekman Spiral (Fig. 6)

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  Ekman viewed the surface ocean under the influence of wind as a series of layers
  
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  a force balance between wind stress, friction and Coriolis forces is attained in the top layer
  
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  for the ‘layers’ below the top layer, the current in the layer above exerts stress on the layer below it, analogous to the wind exerting stress on the top layer, and drags the water in the layer below
  
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  this ‘layering’ implies that the currents in the layer below move to the right in northern hemisphere (and to the left in the Southern Hemisphere) of the direction of the current in the layer above it which is dragging the water along (just like the current in the top layer moves to the right of the wind in the northern hemisphere)
  
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  this causes a spiraling of the current direction with increasing depth in the Ekman layer and is known as the Ekman Spiral
  
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  in reality there is a continuum (rather than series of discrete layers) of currents over depth with each current moving to the right (in northern hemisphere) and at a slower speed than the current above it
  
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  the force exerted by the currents in each deeper layer is less than the force exerted by the current in the layer above because some of this force has been used to overcome frictional resistance to motion in each layer, thus the speed of the currents in the Ekman Spiral decrease with increasing depth
  

11. The direct response of water movement (i.e., currents) to wind stress is restricted to the upper 50 to 100m of the ocean, which is referred to as the Ekman Layer. Below this depth frictional forces are small (negligible) compared to horizontal pressure gradient forces and Coriolis forces.

12. The Ekman Spiral has been observed in the surface layer using a string of current meters (Fig. 7)

-not easy to observe since the current speeds are slow and a constant wind direction is needed

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  that is, if you add up the current speeds and directions of flow of each of the “layers” within the Ekman Spiral, the average water transport direction is perpendicular to the direction of the wind
  
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  this average water flow in the Ekman Layer is called the Ekman Transport and occurs within the upper 50-100m of the ocean
  

14. To calculate the total volume of water transported in the Ekman layer we would multiply the average current speed in the Ekman layer by the cross sectional area defined by the depth of the Ekman layer and the length scale of interest.

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  thus in the Ekman Layer, the volume transport (m³/s) = length scale of interest (m) * Ekman layer depth (m) * average current velocity (m/s)
  
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  typical current velocities in the Ekman layer are 1-5 cm/sec
  

15. Class Calculation: If we took the length scale of interest as the entire width of the Pacific Ocean at 40ºN (i.e., 120° of longitude) and average current velocity of 5 cm/s and Ekman layer depth of 50m, then calculate the volume transport in the Ekman Layer.

Ekman Volume Transport (m³/s) = Cross section area * velocity

= 120° (110km/°)*cos(40°) * (1000m /km) * 50m *0.05 m/s

= 25x10⁶ m³/s

= 25 Sv
-Note that because of the earth’s spherical shape, the east-west distance between lines of longitude decreases poleward. At the equator, there is 110km per degree of longitude. At any other latitude, the east-west distance between longitude lines equals 110km*cos (latitude). [At the limit (poles), when the latitude = 90 º, the cos (90) = 0.]