A Generalized Ekman Model for Frontal Regions
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A Generalized Ekman Model for Frontal Regions Meghan F. Cronin William S. Kessler NOAA Pacific Marine Environmental Laboratory Cronin, M.F. and W.S. Kessler. Near-surface shear flow in the tropical Pacific cold tongue front. Accepted pending minor revision J. Phys. Oceanogr ., 2008. .

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Relevance to climate observing system

A Generalized Ekman Model for Frontal RegionsMeghan F. CroninWilliam S. KesslerNOAA Pacific Marine Environmental LaboratoryCronin, M.F. and W.S. Kessler. Near-surface shear flow in the tropical Pacific cold tongue front. Accepted pending minor revision J. Phys. Oceanogr., 2008.


Relevance to climate observing system

Relevance to Climate Observing System

Ocean System: Upper 25 m is not always slab-like. Surface currents can have significant vertical shear.

Climate Observing System: The Climate Observing System is designed to monitor the 15-m currents. What part of the system monitors the near-surface shear?

Ocean Current Products: The generalized Ekman model can be used in gridding procedures that blend wind-forced current estimates with the geostrophic currents, e.g. OSCAR.

Heat and Freshwater Transport: Calculations of the heat and freshwater transport by the wind-forced Ekman flow depend upon understanding of Ekman flow in frontal regions.


Relevance to climate observing system

Johnson et al. JPO (2001)

Extrapolated above 20m

Neither shipboard, nor moored upward-looking ADCPs measure currents above 20 m. Is there shear above 25m?


Relevance to climate observing system

5m

10m

15m

20m

25m

Sparse network of reference station moorings monitor near-surface shear. Within the TAO/TRITON array, near-surface shear is monitored only at 2 equatorial sites.

An opportunity to measure near-surface currents at 2 °N, 140 °W

  • 5 Sonteks (acoustic Doppler current meters) were placed on a test mooring near the 2ºN,140ºW TAO mooring.

  • Each Sontek had a thermistor.


Relevance to climate observing system

Shear is very sensitive to stratification and mixing. Example: Diurnal Jet

Diurnal composite of wind, temperature, and u-u(25m)

Local time (hours)

north is up

  • At 1600 local, currents at 5 m are 12 cm/s stronger than at 25m and are oriented in direction of wind. Nighttime shear is weak.

  • Even weak daytime restratification can cause diurnal jet.


Relevance to climate observing system

Mean near-surface currents at 2°N, 140°W

  • Zonal flow is westward associated with SEC.

  • Poleward flow is weaker than expected. Inferred transport is less than half that needed to balance expected equatorial upwelling transport.

  • Zonal flow is surface intensified, but poleward current is not. Why?(Slab layer physics should work for both components).


Relevance to climate observing system

Can near-surface shear be considered a combination of Classic Ekman Spiral and geostrophic thermal wind?

∆uag

∆utot

∆ug

Mean for 24-May-2004 to 7-Oct-2004

(Ekman depth Dek= 25 m ?)

Observed ageostrophic currents relative to 25m has Ekman-like spiral 70 to right of wind. But…


Relevance to climate observing system

Can near-surface shear be considered a combination of Classic Ekman Spiral and geostrophic thermal wind? No!

∆uag

∆uag

∆v relative to 25 m (cm s-1)

∆utot

∆ug

∆urelative to 25 m (cm s-1)

Mean for 24-May-2004 to 7-Oct-2004

(Ekman depth Dek= 25 m ?)

(Ekman depth Dek= 80 m)

Observed ageostrophic currents relative to 25m has Ekman-like spiral 70 to right of wind. But…

Classic Ekman spiral has them aligned slightly to the right of the wind stress.


Relevance to climate observing system

“Classic Ekman Model”: Assume steady, linear flow; with uniform density and viscosity; subject to wind stress at surface, no drag at z=-H (-∞). Solves for ua(z).

Equation of motion:

Boundary conditions:


Relevance to climate observing system

“Classic Ekman Model”: Assume steady, linear flow; with uniform density and viscosity; subject to wind stress at surface, no drag at z=-H (-∞). Solves for ua(z).

Equation of motion:

Boundary conditions:


Relevance to climate observing system

Classic Ekman Model (Ekman 1905)Assumes steady, linear flow; with uniform density and viscosity; subject to wind stress at surface, no drag at z=-H (-∞).

Figure from google image

http://www.eeb.ucla.edu/test/faculty/nezlin/PhysicalOceanography.htm


Relevance to climate observing system

“Frontal Ekman Model”: Assume steady, linear flow; with uniform viscosity, subject to wind stress at surface, in a front that is uniform with depth; and withgeostrophic flow at z=-H. Find ua(z).

Equation of motion:

Boundary conditions:


Relevance to climate observing system

“Frontal Ekman Model”: Assume steady, linear flow; with uniform viscosity, in a front that is uniform with depth; subject to wind stress at surface, and geostrophic flow at z=-H. Find ua(z).

Equation of motion:

Boundary conditions:

u = ug + ua

Ekman Spiral is forced by portion of wind stress that is out of balanced with geostrophic shear: eff = 0 - ug/z


Relevance to climate observing system

In frontal region, the ageostrophic Ekman Spiral is forced by the portion of wind stress that is out of balance with surface geostrophic shear: eff = 0 - p

∆uag

∆uag

∆utot

∆v relative to 25 m (cm s-1)

∆utot

∆ug

∆ug

∆urelative to 25 m (cm s-1)

Mean for 24-May-2004 to 7-Oct-2004

Ageostrophic Ekman response depends upon wind stress AND strength and orientation of the front relative to the wind. Ekman response is reduced when winds blow along a front.


Summary

Summary

  • Shear is very sensitive to both the horizontal and vertical temperature distribution.

  • Very weak daytime stratification (<0.2ºC/25m) resulted in a diurnal jet shear of 12 cm/s / 20m on average at 4 PM local!

  • Wind stress balances the TOTAL surface shear (combined geostrophic and ageostrophic shears). The ageostrophic Ekman spiral is forced by the portion of the wind stress that is out of balance with the geostrophic shear.

  • The effect of fronts on Ekman spiral is most pronounced at low latitudes.


Consequences

Consequences

=

Ekman Transport

in Frontal Region

  • In frontal region, Ekman transport is not necessarily to right of the wind stress. Traditional Ekman heat transport implicitly assume that viscosity decays with depth.

  • For 2ºN, 140ºW, southeasterly trades blowing across the cold-tongue front result in weaker than expected poleward currents. There may be a secondary circulation associated with the front, with downwelling on the cold side and upwelling on the warm side of the front.


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