Gyre Circulation and Western Boundary Currents

1. Gyre Circulation and Western Boundary Currents Lecture 15 OEAS-604 November 14, 2011 • Outline: • Atmospheric Circulation and Global Wind Patterns • Ekman Pumping • Vorticity • Sverdrup Transport • Intensification of Western Boundary Currents

2. The Coriolis Effect Influences the Movement of Air in Atmospheric Circulation Cells Global air circulation as described in the six-cell circulation model. Air rises at the equator and falls at the poles, but instead of one great circuit in each hemisphere from equator to pole, there are three in each hemisphere. Note the influence of the Coriolis effect on wind direction. The circulation show here is idea – that is, a long-term average of wind flow.

3. Global Wind Patterns In a very general way, wind can be presented simply by east-west variability

4. Major Sub-tropical Gyres

5. North Atlantic Gyre

6. North Pacific Gyre

7. Indian Ocean Gyre

8. From a previous lecture we show that the Ekman spiral comes from the following simplified balance: Which is the same thing as: So the mass transport associated with this is: So ignoring the north-south component of the wind, we can represent the winds over the North Atlantic as: 0.1 N/m2 40°N y = L Idealized representation of North Atlantic with wind forcing 30°N Wind stress -0.1 N/m2 20°N y = -L 80°W 20°W

9. For Gyre Circulation, convergence in Ekman transport is caused by the wind stress curl. Ekman Transport

10. Convergence piles up water in the center and leads to downwelling or “Ekman Pumping”

11. wind east 40°N 20°N north WE Convergence due to surface Ekman transport leads to downward velocity. This is called “Ekman pumping.” The vertical velocity from Ekman pumping (WE) can be derived simply from continuity, ignoring any gradients in transport in the x-direction (east-west):

12. Vorticity or Angular Momentum Just like the momentum equations we have already derived, angular momentum must be conserved. There are two types of vorticity: 1) Relative vorticity; 2) Planetary vorticity Relative Vorticity (relative to Earth) Positive Vorticity (northern hemisphere) Negative Vorticity (northern hemisphere)

13. Conservation of Momentum (including angular momentum or vorticity) only applies to inertial reference frame. But Earth is rotating. Vorticity associated with the rotating earth is called Planetary Vorticity

14. Just like the Coriolis parameter, planetary vorticity is a function of latitude. North Pole Consider a parcel of water at the North Pole. It is rotating counter-clockwise relative to the stars. If the parcel of water is moved toward the equator it will appear to be rotating counter-clockwise relative to the surrounding water.

15. Conservation of Vorticity: Planetary vorticity Relative vorticity Constant Height of water column In the example on the previous slide, if the height of the water column does not change as a parcel of water is moved toward the equator, the decrease in planetary vorticity must be balanced by the increase in relative vorticity.

16. Stretching a column of water increases its relative vorticity. Squashing a column of water decreases its relative vorticity. Constant In northern hemisphere, if you squash a parcel of water, it can either 1) rotate slower; or 2) move to the south where planetary vorticity is lower.

17. However, in the open ocean away from boundaries, squashing or stretching a water column does not tend to produce relative vorticity. Instead, water moves north or south until the coriolis parameter is sufficient to balance vorticity. wind east 40°N 20°N north Sverdrup Transport: where: Anywhere that the vertical velocity is negative (downward), the water column is being squashed. This will cause the water to move south in order to find region with lower planetary vorticity. This is called Sverdrup transport.

18. Sverdrup’s Solution Predicted the North-South Flow Caused by Ekman Pumping. divergence divergence convergence convergence The patterns of convergence and divergence necessitate that there be a compensating east-west flow. Sverdrup’s solution only hinted that there must be an intense western boundary current. However, his solution did not have friction at the boundaries.

19. Stommel’s solution. With constant Coriolis With variable Coriolis Stommel showed that the intensification of the western boundary current was a direct consequence in the variation in the Coriolis Parameter.

20. Stommel’s solution is best explained in terms of vorticitiy dynamics. Everywhere over the basin, the wind stress is adding negative vorticity. At both the eastern and western boundary, friction is adding positive vorticity So if the Coriolis force was constant the negative vorticity input from the wind could be balanced by the positive vorticity input of friction on both sides of the basin. + -

21. But Coriolis force is a function of Latitude North Pole North Pole Moving south, parcels spins (counter clockwise) faster, thus it gains positive vorticity. Moving north, parcels spins (counter clockwise) slower, thus it gains negative vorticity.

22. Stommel’s solution is best explained in terms of vorticitiy dynamics. Everywhere over the basin, the wind stress is adding negative vorticity. Moving north, flow gains negative vorticity. Moving south, flow gains positive vorticity. At both the eastern and western boundary, friction is adding positive vorticity + = = + At western boundary, both the wind and changing Coriolis force impart negative vorticity. Only way for this to balance is if friction is big. This requires fast current