Spiral of Ekman

The spiral of Ekman is the result of the structure of the currents in a fluid in rotation (air, water, etc) close to a solid boundary. For example, the change of management and speed of the winds in the layer close to the ground is a spiral of Ekman.

Origin

During an oceanographical forwarding in the Arctic Ocean, Norwegian Fridtjof Nansen, on board the Fram , observed that the displacement of the icebergs subjected to the wind did not follow the direction of this one. Indeed, they derived from 45 degrees towards the line. Of return of its forwarding, in 1886, it shared its knowledge and its observations with Swedish Vagn Walfrid Ekman. Ten years later, towards 1905, Ekman published the theory of this model of circulation, called Spirale of Ekman.

In the atmosphere

The spiral is a consequence of the Force of Coriolis, Viscosité of the Fluide and Friction of surface border. A fluid as the air which is in a reference frame in rotation undergoes two forces: the difference in pressure which forces it to move towards the lowest pressures and the force of Coriolis.

The movement is initially printed by the compressive force, the mass of air " chutant" in the puit of depression. The force of Coriolis, which is not a real force but the result of the rotation of the Ground on the movement of a particle such as sight by an observer on the ground, " dévie" substantively this movement perpendicular to the air volume displacement. In the northern hemisphere, the deviation is towards the line while looking towards the depressionary center. With balance, the current circulates along the Isobare S, without friction. This phenomenon is described by the equations of the Vent geostrophic which reveals in particular the periodicity of such structures: a Wave of Rossby.

It is what one sees in the higher part left of the figure opposite and it is roughly what occurs in the Troposphère above the layer where the friction of the ground is exerted (500 m to 3 km thickness according to the ground). However, in this Boundary layer, the friction is added to the balance of power (left in left bottom of the drawing) but direction opposed to displacement. This slows down the mass of air which consequently falls into the depressionary puit (just as a satellite in broken down low orbit of engine would fall on surface from the ground by friction with its atmosphere).

The right part of the drawing shows us the variation speed in amplitude and direction according to altitude. The friction is maximum on the ground and its effect, propagated by the viscosity of the fluid, decreases to zero gradually while rising. Thus the direction of the winds turns towards the left, by facing the depressionary center in the northern hemisphere, between the top of the boundary layer and the ground.

Surface air-water

The figure of right-hand side shows the effect of the spiral of Ekman on the air-to-sea interface. There is a wind which puts moving water surface by friction. The force of Coriolis makes deviate towards the line the current thus induced. This surfacing makes move the layer subjacent but at a lower speed because of dissipation by viscosity. This new displacement is him also deviated towards the line by the force of Coriolis. The thickness of the layer affected by the spiral depends on the viscosity of the sea and is called the layer of Ekman .

There is thus an opposite variation of direction of that mentioned in the air for two reasons:

  • the friction is at the top of the layer of water instead of its base
  • the movement is not due to a balance between the force of Coriolis and the gradient of pressure but to the transfer of movement by the wind.

There is in this case a intertielle trajectory (see Inertias) where only the force of Coriolis acts. In the sea, the spiral of Ekman is especially observed in covered water of ice where the Thermocline is stable, reducing viscosity. On the open sea, the thermocline varying in a diurnal way and the waves do not allow the propagation of in-depth movement, generated turbulence dissipates the effect of the spiral quickly.

Related consequences and phenomena

See also: Transport of Ekman

Norwegian Otto Sverdrup tried to apply this theory to a oceanic basin, within a subtropical gyre anticyclonic. He thus showed that water fills up in the center of the subtropical gyre and that causes the birth of a convergence in the center of the basin. This convergence forms a dome which can rise of one meter to the top of the sea. In the case of a cyclonic gyre, the opposite phenomenon is carried out, creating a zone of divergence, in the center of the gyre, causing a deep water increase to compensate for the local fall of the sea level.

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