Ekman spiral

Ekman spiral effect.
1. Wind
2. force from above
3. Effective direction of the current
4. Coriolis effect

The Ekman spiral is a structure of currents or winds near a horizontal boundary in which the flow direction rotates as one moves away from the boundary. It derives its name from the Swedish oceanographer Vagn Walfrid Ekman. The deflection of surface currents was first noticed by the Norwegian oceanographer Fridtjof Nansen during the Fram expedition (1893–1896) and the effect was first physically explained by Vagn Walfrid Ekman.[1]

Theory

The effect is a consequence of the Coriolis effect which subjects moving objects to an apparent force to the right of their direction of motion in the northern hemisphere (and to the left in the Southern Hemisphere). Thus, when a persistent wind blows over an extended area of the ocean surface in the northern hemisphere, it causes a surface current which accelerates in that direction, which then experiences a Coriolis force and acceleration to the right of the wind: the current will turn gradually to the right as it gains speed. As the flow is now somewhat right of the wind, the Coriolis force perpendicular to the flow's motion is now partly directed against the wind. Eventually, the current will reach a top speed when the force of the wind, of the Coriolis effect, and the resistant drag of the subsurface water balance, and the current will flow at a constant speed and direction as long as the wind persists. This surface current drags on the water layer below it, applying a force in its own direction of motion to that layer, repeating the process whereby that layer eventually becomes a steady current even further to the right of the wind, and so on for deeper layers of water, resulting in a continuous rotation (or spiraling) of current direction with changing depth. As depth increases, the force transmitted from the driving wind declines and thus the speed of the resultant steady current decreases, hence the tapered spiral representation in the accompanying diagram. The depth to which the Ekman spiral penetrates is determined by how far turbulent mixing can penetrate over the course of a pendulum day.[2]

The diagram above attempts to show the forces associated with the Ekman spiral as applied to the Northern hemisphere. The force from above is in red (beginning with the wind blowing over the water surface), the Coriolis force (which is shown at right angles to the force from above when it should in fact be at right angles to the actual water flow) is in dark yellow, and the net resultant water movement is in pink, which then becomes the force from above for the layer below it, accounting for the gradual clockwise spiral motion as you move down.

Observation

The first documented observations of an oceanic Ekman spiral were made in the Arctic Ocean from a drifting ice flow in 1958.[3] More recent observations include:

• SCUBA diving observations during a study of upwelling water transport through a kelp forest on the west coast of South Africa in 1978 [4]
• The 1980 Mixed Layer Experiment[5]
• Within the Sargasso Sea during the 1982 Long-Term Upper Ocean Study [6]
• Within the California Current during the 1993 Eastern Boundary Current experiment [7]
• Within the Drake Passage region of the Southern Ocean [8][9]
• North of the Kerguelan Plateau during the 2008 SOFINE experiment [10]

Common to several of these observations spirals were found to be 'compressed', displaying larger estimates of eddy viscosity when considering the rate of rotation with depth than the eddy viscosity derived from considering the rate of decay of speed.[6][7][8] Though in the Southern Ocean the 'compression', or spiral flattening effect disappeared when new data permitted a more careful treatment of the effect of geostrophic shear.[9][10]

The classic Ekman spiral has been observed under sea ice,[3] but observations remain rare in open-ocean conditions. This is due both to the fact that the turbulent mixing in the surface layer of the ocean has a strong diurnal cycle and to the fact that surface waves can destabilize the Ekman spiral. Ekman spirals are also found in the atmosphere. Surface winds in the Northern Hemisphere tend to blow to the left of winds aloft.

Notes

1. ^ Ekman, V. W. 1905. On the influence of the Earth's rotation on ocean currents. Arch. Math. Astron. Phys., 2, 1-52. [1]
2. ^ "AMS Glossary". Archived from the original on 2007-08-17. Retrieved 2007-06-28.
3. ^ a b Hunkins, K. (1966). "Ekman drift currents in the Arctic Ocean". Deep-Sea Research. 13 (4): 607–620. Bibcode:1966DSROA..13..607H. doi:10.1016/0011-7471(66)90592-4.
4. ^ Field, J. G., C. L. Griffiths, E. A. S. Linley, P. Zoutendyk and R. Carter (1981). Wind-induced water movements in a Benguela kelp bed. Coastal Upwelling. F. A. Richards (Ed.), Washington D.C., American Geophysical Union: 507-513. ISBN 0-87590-250-2
5. ^ Davis, R.E.; de Szoeke, R.; Niiler., P. (1981). "Part II: Modelling the mixed layer response". Deep-Sea Research. 28 (12): 1453–1475. Bibcode:1981DSRI...28.1453D. doi:10.1016/0198-0149(81)90092-3.
6. ^ a b Price, J.F.; Weller, R.A.; Schudlich, R.R. (1987). "Wind-Driven Ocean Currents and Ekman Transport". Science. 238 (4833): 1534–1538. Bibcode:1987Sci...238.1534P. doi:10.1126/science.238.4833.1534. PMID 17784291. S2CID 45511024.
7. ^ a b Chereskin, T.K. (1995). "Direct evidence for an Ekman balance in the California Current". Journal of Geophysical Research. 100 (C9): 18261–18269. Bibcode:1995JGR...10018261C. doi:10.1029/95JC02182.
8. ^ a b Lenn, Y.-D.; Chereskin, T.K. (2009). "Observation of Ekman Currents in the Southern Ocean". Journal of Physical Oceanography. 39 (3): 768–779. Bibcode:2009JPO....39..768L. doi:10.1175/2008jpo3943.1.
9. ^ a b Polton, J.A.; Lenn, Y.-D.; Elipot, S.; Chereskin, T.K.; Sprintall, J. (2013). "Can Drake Passage Observations Match Ekman's Classic Theory?" (PDF). Journal of Physical Oceanography. 43 (8): 1733–1740. Bibcode:2013JPO....43.1733P. doi:10.1175/JPO-D-13-034.1.
10. ^ a b Roach, C.J.; Phillips, H.E.; Bindoff, N.L.; Rintoul, S.R. (2015). "Detecting and Characterizing Ekman Currents in the Southern Ocean". Journal of Physical Oceanography. 45 (5): 1205–1223. Bibcode:2015JPO....45.1205R. doi:10.1175/JPO-D-14-0115.1.

References

• AMS Glossary, mathematical description
• A. Gnanadesikan and R.A. Weller, 1995 · "Structure and instability of the Ekman spiral in the presence of surface gravity waves" · Journal of Physical Oceanography  25(12), pp. 3148–3171.
• J.F. Price, R.A. Weller and R. Pinkel, 1986 · "Diurnal cycling: Observations and models of the upper ocean response to diurnal heating, cooling and wind mixing" · Journal of Geophysical Research  91, pp. 8411–8427.
• J.G. Richman, R. deSzoeke and R.E. Davis, 1987 · "Measurements of near-surface shear in the ocean" · Journal of Geophysical Research  92, pp. 2851–2858.
• Field, J. G., C. L. Griffiths, E. A. S. Linley, P. Zoutendyk and R. Carter, 1981 Wind-induced water movements in a Benguela kelp bed. Coastal Upwelling. F. A. Richards (Ed.), Washington D.C., American Geophysical Union: 507–513. ISBN 0-87590-250-2

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