Ekman Layer

The Ekman layer (EL) is boundary near-surface layer in the low troposphere and upper ocean, in which the vertical turbulent friction plays a crucial role in the balance of governing forces. Ekman transport is to the right or left of the wind in the Northern or Southern Hemisphere, respectively. This causes upwelling along the equator and certain coastlines.

As V. W. Ekman showed in his classic 1905 paper, “On the Influence of the Earth’s Rotation on Ocean Currents,” the basic steady balance within the EL (in the ocean where depth can be considered infinite) occurs between vertical friction and the Coriolis force. Such balance leads to the generation of the Ekman spiral of drift current (wind). This spiral is a result of turning and weakening of the Ekman current (or wind) to the depth (upper boundary of the EL in the atmosphere).

The vector of Ekman current (wind) is rotating clockwise/anticlockwise to the depth (in the atmospheric boundary layer) in the Northern and Southern Hemisphere. The angle between vectors of surface Ekman current and surface wind is equal to 45 degrees, if the coefficient of vertical turbulent exchange (mixing) does not depend on the depth, as was postulated in the classic Ekman theory. In fact, this angle is usually close to 30 degrees because the coefficient of vertical turbulent mixing decreases to the depth.

In the deep ocean, EL thickness (or Ekman scale) is determined as a depth, where the current direction is opposite to the surface direction. Speed of drift current at the low boundary of EL is smaller than surface speed by eπ times. Thickness of EL in the homogeneous fluid (gas) is controlled by two parameters: (1) turbulent stress (or dynamic velocity depending on the wind speed) at the sea surface, and (2) Coriolis parameter. Wind in the mid-latitudes, of which the speed is about 33 ft. (10 m) per second, generates the surface drift current of about 12 in. (30 cm) per second. The corresponding Ekman scale is about 98 ft. (30 m).

In the ocean at intermediate depth (ocean depth and Ekman scale are the same order), the Ekman spiral is modified, and rotation of current vector to the depth decreases. Typical temporal scale of steady Ekman spiral development is equal to local inertial period. For instance, classic Ekman balance in the mid-latitude interior of the upper ocean is established in about one day after the beginning of wind forcing.

There is also a bottom EL in the ocean, which should be taken into account in the global circulation models if the ocean’s depth is not too large in comparison with the Ekman scale, or for super high-resolved models with a typical size of the vertical grid in the bottom layer of about 33 ft. (10 m). Special care should be taken for the case of a shallow sea, where the depth is much smaller than the Ekman scale. In this case, surface and bottom ELs create a unique EL in which turbulence is well developed, while the Coriolis term is small. As a result, the rotation of drift current to the depth is negligible, and directions of surface wind and drift current in the shallow ocean coincide.

From comprehensive analysis provided by Eric Kraus, Andrey Monin, and Alexander Yaglom, it has been shown that in the stratified fluid (gas), a depth of mixed turbulized layer may be much smaller than EL thickness because turbulent stress is working against buoyancy force. In this case, profile of velocity within the mixed layer looks like a drift current in the shallow sea. Transport of drift (Ekman) current in the ocean’s interior (i.e., in the deep ocean) does not depend on the coefficient of vertical turbulent exchange. It can be calculated quite accurately if the surface wind stress and latitude of the area is known. For instance, based on the assessment by Eric Kraus and Sid Levitus, integral meridional volume transport of drift current across a latitude circle in the world ocean associated with the trade winds reaches about 50 Sverdrups (1 Sverdrup = 106 cu. m per second) and accounts for a significant proportion of meridional overturning circulation within the tropics and at the boundary between tropics and subtropics.