Ekman developed the theory of the Ekman layer after Fridtjof Nansen observed that ice drifts at an angle of 20°-40° to the right of the prevailing wind direction while on an Arctic expedition aboard the Fram. Nansen asked his colleague, Vilhelm Bjerknes to set one of his students upon study of the problem. Bjerknes tapped Ekman, who presented his results in 1902 as his doctoral thesis.
Mathematical formulation 
The mathematical formulation of the Ekman layer can be found by assuming a neutrally stratified fluid, with horizontal momentum in balance between the forces of pressure gradient, Coriolis and turbulent drag.
Boundary conditions 
There are many regions where an Ekman layer is theoretically plausible; they include the bottom of the atmosphere, near the surface of the earth and ocean, the bottom of the ocean, near the sea floor and at the top of the ocean, near the air-sky interface.
where and are the components of the surface stress, , of the wind field or ice layer at the top of the ocean and and are the geostrophic flows in the and directions – as
These differential equations can be solved to find:
This variation of horizontal velocity with depth () is referred to as the Ekman spiral, diagrammed above.
By applying the continuity equation we can have the vertical velocity as following
Note that when vertically integrated the volume transport associated with the Ekman spiral is to the right of the wind direction in the Northern Hemisphere.
Experimental observations of the Ekman layer 
There is much difficulty associated with observing the Ekman layer for two main reasons: the theory is too simplistic as it assumes a constant eddy viscosity, which Ekman himself anticipated, saying
|“||It is obvious that cannot generally be regarded as a constant when the density of water is not uniform within the region considered||”|
and because it is difficult to design instruments with great enough sensitivity to observe the velocity profile in the ocean.
In the atmosphere 
In the atmosphere, the Ekman solution generally overstates the magnitude of the horizontal wind field because it does not account for the velocity shear in the surface layer. Splitting the boundary layer into the surface layer and the Ekman layer generally yields more accurate results.
In the ocean 
The Ekman layer, with its distinguishing feature the Ekman spiral, is rarely observed in the ocean. The Ekman layer near the surface of the ocean extends only about 10 – 20 meters deep, and instrumentation sensitive enough to observe a velocity profile in such a shallow depth has only been available since around 1980. Also, wind waves modify the flow near the surface, and make observations close to the surface rather difficult.
Observations of the Ekman layer have only been possible since the development of robust surface moorings and sensitive current meters. Ekman himself developed a current meter to observe the spiral that bears his name, but was not successful. The Vector Measuring Current Meter  and the Acoustic Doppler Current Profiler are both used to measure current.
The first documented observations of an Ekman-like spiral were made in the Arctic Ocean from a drifting ice flow in 1958. More recent observations include:
- The 1980 Mixed Layer Experiment
- Within the Sargasso Sea during the 1982 Long Term Upper Ocean Study 
- Within the California Current during the 1993 Eastern Boundary Current experiment 
- Within the Drake Passage region of the Southern Ocean 
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.
See also 
- [Benoit] (1994). "Chapter 5 - The Ekman Layer". Introduction to Geophysical Fluid Dynamics (1st ed.). Prentice Hall. pp. 76–77. ISBN 0-13-353301-8.
- [Geoffrey K.] (2006). "Chapter 2 – Effects of Rotation and Stratification". Atmospheric and Oceanic Fluid Dynamics (1st ed.). Cambridge, UK: Cambridge University Press. pp. 112–113. ISBN 0-521-84969-1.
- Ekman, V.W. (1905). "On the influence of the earth's rotation on ocean currents". Ark. Mat. Astron. Fys. 2 (11): 1–52.
- [James R.] (2004). "Chapter 5 – The Planetary Boundary Layer". Dynamic Meteorology. International Geophysics Series 88 (4th ed.). Burlington, MA: Elsevier Academic Press. pp. 129–130. ISBN 0-12-354015-1.
- Santala, M. J.; Terray, E. A. (1992). "A technique for making unbiased estimates of current shear from a wave-follower". Deep-Sea Res. 39 (3–4): 607–622. Bibcode:1992DSRI...39..607S. doi:10.1016/0198-0149(92)90091-7.
- Rudnick, Daniel (2003). "Observations of Momentum Transfer in the Upper Ocean: Did Ekman Get It Right?". Near-Boundary Processes and their Parameterization (Manoa, Hawaii: School of Ocean and Earth Science and Technology).
- Weller, R.A.; Davis, R.E. (1980). "A vector-measuring current meter". Deep-Sea Res. 27 (7): 565–582. Bibcode:1980DSRI...27..565W. doi:10.1016/0198-0149(80)90041-2.
- Hunkins, K. (1966). "Ekman drift currents in the Arctic Ocean". Deep-Sea Res. 13: 607–620.
- Davis, R.E.; de Szoeke, R.; Niiler., P. (1981). "Part II: Modelling the mixed layer response". Deep-Sea Res. 28 (12): 1453–1475. Bibcode:1981DSRI...28.1453D. doi:10.1016/0198-0149(81)90092-3.
- Price, J.F.; Weller, R.A.; Schudlich, R.R. (1987). "Wind-Driven Ocean Currents and Ekman Transport". Science 238: 1534–1538. Bibcode:1987Sci...238.1534P. doi:10.1126/science.238.4833.1534.
- Chereskin, T.K. (1995). "Direct evidence for an Ekman balance in the California Current". Journal of Geophysical Research 100: 18261–18269. Bibcode:1995JGR...10018261C. doi:10.1029/95JC02182.
- Lenn, Y; Chereskin, T.K. (2009). "Observation of Ekman Currents in the Southern Ocean". Journal Of Physical Oceanograph 39: 768–779.