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Ekman Dynamics

Ekman Dynamics. Lecture 13. OEAS-604. November 7, 2011. Outline: Review of Geostrophic Balance and Scaling Ekman Number and Mixing Time Scale Wind-driven Currents The Ekman Layer and Ekman Spiral Upwelling. So far we have focused the geostrophic balance :.

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Ekman Dynamics

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  1. Ekman Dynamics Lecture 13 OEAS-604 November 7, 2011 • Outline: • Review of Geostrophic Balance and Scaling • Ekman Number and Mixing Time Scale • Wind-driven Currents • The Ekman Layer and Ekman Spiral • Upwelling

  2. So far we have focused the geostrophic balance: But, this ignores Friction. When is friction important? Scaled form of X-momentum: Rossby Number: Flow can only be considered geostrophic when both the Rossby and Ekman numbers are small. Ekman Number: Assuming Lx = Ly

  3. Another way of thinking about it is how long would it take for turbulent mixing from the surface to penetrate to a given depth. A back of envelope mixing time scale is given as: Assuming that Az ~ 10-2 m2/s how long would it take to deepen the surface mixed layer

  4. When are rotation and friction equally important? Scaled form of X-momentum: Ekman Number: Assuming Lx = Ly When Ekman number is ~ 1. Since the source of the mixing in most of the ocean is at surface due to winds, both rotation and friction are important only near the surface. So, if Az = 10-2 m2/s and f = 10-4 s-1, than both rotation and friction are important for areas on the order of 10s of meters near the surface.

  5. Wind blowing over the surface of the ocean transfers momentum from the wind to the ocean, driving surface currents. fast Wind ~ 10 m/s friction Momentum is transported down-gradient slow Current < 1 m/s slower slowest Flux of momentum is a stress at the surface is called the surface stress or wind stress:

  6. OK, so if the Ekman number is on the order of 1, both friction and rotation are important. What happens when both rotation and friction are important? First consider the case without rotation and ignoring pressure gradients for now t = T1; wind begins to blow toward the north t = T2; wind continues to blow t = 0; no wind, no motion wind wind drag (friction) drag (friction) Friction increases to balance wind stress, no more acceleration Imbalance between wind stress and frictional drag cause flow to accelerate

  7. But Earth is Rotating wind wind Coriolis Coriolis drag (friction) drag (friction) Current deflects to the right, changing direction of both Coriolis force and drag force Forces don’t balance so flow accelerated to the right of the wind. Wind stress acts to accelerate the parcel to the north. Friction drag always acts opposite of the direction of motion. Coriolis always acts to right of motion.

  8. Flow continues to deflect to the right until all forces are in balance. wind drag (friction) Coriolis Result is a surface current that is 45 degrees to the right of the wind

  9. Think about the ocean as composed of a series of layers. wind Wind only acts on surface layer drag (friction) Coriolis overlying current Resulting current drag (friction) Coriolis Subsurface layers get momentum from overlying layer, not directly from wind.

  10. Ekman Spiral: • The water can be thought of as a set of vertical layers • The top layer is driven forward by the wind and each layer below is moved by friction (momentum flux). • There is a divergence in momentum flux, so each layer gets slower than the overlying layer • Just like the surface layer gets momentum from the wind, each layer gets momentum from the layer above it. • In order for the forces to balance on each layer, the flow must continue to deflect to the right as you move down the water column.

  11. Mathematically this was first derived by Vagn Walfrid Ekman in 1905 Ekman assumed simple balance between friction and rotation: x and y momentum balances: Definition of surface stress For simplicity we are going to assume no stress in x direction (E-W), so wind is to the north (doesn’t really matter) The solution: where:

  12. The solution gives the Ekman Spiral: where: This is called the Ekman Depth– the depth at which the current is opposite of the surface current This is the magnitude of the surface velocity

  13. Even thought the surface current is 45 degrees to the right of the wind direction, the integrated transport is 90 degrees to the right of the wind (in northern hemisphere).

  14. What are the consequences for wind-driven Ekman transport?

  15. Coastal Upwelling Can Lead to High Biological Productivity

  16. Equatorial Upwelling NORTH View from above Ekman Transport N.E. Trade Winds Equator S.E. Trade Winds Ekman Transport SOUTH Equator Warm nutrient poor waters NORTH SOUTH Cold nutrient rich waters

  17. Upwelling Velocity

  18. Equatorial Upwelling Leads to High Biological Productivity Increased Biology Colder “upwelled” water

  19. What happens if there are gradients in wind stress? Lateral gradients in wind stress are often called the “wind stress curl” and can lead to upwelling/downwelling Wind stress curl terms.

  20. “Gap winds” along the coast of Central America can lead to strong wind stress curl.

  21. Gap winds can lead to strong upwelling Tehuantepec Winds Papagayo Winds Sea Surface Temperature from Sattelite

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