# Corkscrew flow

Representation of an Ekman spiral in the northern hemisphere. Above in perspective, in the middle the top view, below the balance of forces for a layer.

The corkscrew current , also known as the Ekman spiral (after Vagn Walfrid Ekman ) is a vertical speed profile that occurs in the ocean away from the equator, where wind blows steadily over an extensive body of water . In total - over the depth range of the Ekman spiral - water is transported across the wind direction. This is essential for understanding wind-driven circulation , see Evidence and Significance of Ekman Transport . The same occurs as an Ekman layer in the atmosphere between about 100 and 1000 altitude.

## description

The wind pulls the water with it through friction . Its movement is deflected by the Coriolis force , to the right in the northern hemisphere . Each deeper layer of water is dragged along by the one above and slowed down by the one below. The different directions and amounts of the frictional forces just compensate for the Coriolis force on the layer under consideration. This condition means that deeper water layers move more and more slowly and the direction of movement deviates more and more from the wind direction . More precisely, the speed vectors form a logarithmic spiral with

${\ displaystyle | v | = e ^ {- \ alpha}}$

In it is

• ${\ displaystyle e}$the Euler's number and
• ${\ displaystyle \ alpha}$the angle of revolution in radians .

After half a revolution, the speed has decreased to a fraction . ${\ displaystyle | v |}$${\ displaystyle e ^ {- \ pi} \ approx 1/23}$

The depth of the spiral results from the viscosity and density of the water and the vertical component of the rotation speed. In the so-called Ekman depth - in the middle geographical latitudes around fifty meters - the water flows in the opposite direction to the wind direction. This is considered to be the limit of the influence of wind friction.

The surface flow is rotated 45 ° to the wind direction and reaches around three percent of the wind speed .

Just as there is an Ekman spiral on the surface of the water, there is also an Ekman spiral in the air above the surface of the water or above the ground or in the water above the sea floor if this water is flowing. This has a reverse sense of rotation. The resulting speed turns to the left with greater depth (in the northern hemisphere). The two spirals overlap in shallow water. If the water is shallow enough, the resulting surface flow points in the direction of the wind.

## literature

• Ekman, VW, 1905. On the influence of the earth's rotation on ocean currents. Arch. Math. Astron. Phys. 2, No. 11
• Schudlich, RR, Price, JF, 1998. Observations of Seasonal Variation in the Ekman Layer. J. Phys. Oceanogr., (Volume) 28, 6, p1187–1204