The Ekman spiral and Langmuir circulation

The orbital motion of water induced by surface waves penetrates some metres beneath the sea surface. The direct effect of the wind, however, penetrates to a depth of scores of metres. This is because of a larger scale physical force balance than the microscale pressure anomalies causing wave motion. The resulting flow varies with depth in the Ekman spiral. Small-scale circulation cells driven by this spiral are known as Langmuir circulation cells.

2.10.1 The Ekman spiral

In the winter of 1893/4 Fridtjof Nansen's vessel, Fram, was stuck fast in the Arctic ice pack, 500 km north of Russia. This was not due to poor seamanship, but a deliberate attempt, using a specially designed vessel, to undertake scientific study of the Arctic during the inhospitable winter. The ice voyage was also used to give a northerly launching point for Nansen and Johansen's unsuccessful attempt to reach the North Pole.

The Fram slowly drifted in a westward direction, the ice being pushed by the prevailing near-surface ocean current. Nansen observed that the ice usually moved at an angle of 20-40° to the right of the wind direction. On his return to Norway he discussed this phenomenon with Ekman, who developed a theory to explain it.

We saw in §2.8 that the wind exerts a stress on the ocean surface. Orbital wave motion enables the upper ocean to act as a series of layers. The stress transmitted to the surface layer by the wind forces motion in the layer below, through the stress at the layer interface. This passes momentum to a further layer, so driving flow in a succession of layers, as shown in Fig. 2.27. Each layer dissipates energy through internal friction, allowing the wind stress to penetrate only so far into the ocean - this depth defines the Ekman layer. As each layer is moving it is subject to the Coriolis force, which will deflect its motion to the right in the Northern Hemisphere. If the wind has been blowing with the same strength and direction for some time, our observation point is far from land so that coastal effects do not modify the flow, and if the water is of uniform density, then, for a steady flow, there must be a force balance between the wind stress and the net Coriolis force integrated over the Ekman layer. This is illustrated in Fig. 2.27.

5 While sea salt is a major aerosol, sulphate and organic carbon form the majority of the actual particles. These, however, have much smaller radii. The formation, and importance, of these smaller cloud condensation nuclei will be considered in Chapters 4 and 7.

Fig. 2.27. Schematic of the effect of a steady wind blowing over the surface of the ocean. Over the Ekman layer successive layers of the water frictionally induce motion in the layer beneath, until no energy remains. Each layer's motion is subject to the Coriolis force; the net Coriolis force over the total column opposes the surface wind stress giving the Ekman transport of the layer - the net motion of the column as a whole - to the right of the wind in the Northern Hemisphere. [After Fig. 3.6 of Open University Course Team (1989). Adapted with permission of

Butterworth-Heinemann Ltd.]

Wind Ekman Spiral

The resulting net flow over the Ekman layer is therefore at right angles to the forces - just as for the geostrophic velocity discussed in §2.6.3 - and to the right of the wind in the Northern Hemisphere. This net flow is known as the Ekman transport, and is a very important principle for understanding the surface ocean circulation, as we will see in §2.11.

Just as the wind exerts a stress on the water surface we saw in §2.8 that the ocean exerts a stress or drag on the atmosphere. The same physical argument can therefore be applied to the atmospheric boundary layer, even over land. An Ekman layer is thus present in the atmosphere, with the force balance acting in the opposite direction to give the atmospheric Ekman transport a backing to the left in the Northern Hemisphere. To balance the oceanic stress, the atmospheric Ekman mass transport will be the same as the oceanic. However, the volume transport will be much greater because of the large density difference between air and water. The atmospheric Ekman layer is thus significantly deeper than the oceanic layer, reaching perhaps a kilometre in height.

In Fig. 2.27 the surface current is shown directed at an angle of 45° to the wind. This direction was predicted by Ekman and is caused by the influence of viscosity near the surface, where there are strong vertical current shears. The surface current is actually aligned with the geostrophic wind velocity, but the friction of the air with the surface causes the surface air velocity to deviate, as discussed in §2.6. As Nansen observed, the surface current is rarely, if ever, at its theoretical orientation relative to the wind. The Ekman spiral is almost always concealed from view by temporal variability in the wind field, the effect of interaction with coasts or the sea floor, and also by the currents driven by density differences within the ocean. The net Ekman transport is nevertheless generally observed as a vital feature of the upper ocean circulation.

Fig. 1.6 showed the mean circulation of the lower atmosphere. If we regard this as steady over several months, so that the balance leading to the Ekman spiral can be established, the variation of wind speed and direction with position will create zones where Ekman transports from different directions will oppose. For instance, over the sub-tropical oceans the anticyclonic atmospheric circulation

Fig. 2.28. Net Ekman transport for sub-tropical oceans in the Northern Hemisphere. The anticyclonic surface winds (a) produce net inflow of water towards the centre of the sub-tropical high pressure centres. This drives convergence (b) and downwelling of water in the centre of the oceanic gyre, both raising the sea surface, and depressing the thermocline. [After Fig. 3.23b of Open University Course Team (1989). Adapted with permission of

Butterworth-Heinemann Ltd.l

Ekman Pumping

will induce Ekman transports towards the centre of the anticyclone, as shown in Fig. 2.28. This will produce convergence, with a doming of the sea surface and consequent sinking of water. This downwelling is known as Ekman pumping and the resulting vertical velocity can be shown to depend on the horizontal gradients in the wind stress. Although this vertical velocity is generally less than 0.5 m/day it is the main contributor to vertical motion in the upper ocean. During strong storms or hurricanes, when winds change strikingly over small distances, Ekman pumping can be considerable. In Chapters 3 and 4 we will see the importance of vertical motion for chemical and biological processes of climatic relevance; §2.4.2 has already referred to this.

2.10.2 Langmuir circulation

If you have flown in an aircraft over the sea, or been able to observe a lake from surrounding mountains you will probably have observed parallel streaks of foamy water, 30-50 m apart, extending hundreds of metres across the water. A photographic example is shown in Fig. 2.29. These are the surface signatures

Fig. 2.29. Photograph of streak lines associated with foam convergence along the wind-rows of Langmuir circulation cells. [Fig. 3.26b of Open University Course Team (1989). Reproduced with permission of Butterworth-Heinemann Ltd.]

Fig. 2.29. Photograph of streak lines associated with foam convergence along the wind-rows of Langmuir circulation cells. [Fig. 3.26b of Open University Course Team (1989). Reproduced with permission of Butterworth-Heinemann Ltd.]

Windrows WaterLake Water Langmuir
Fig. 2.30. Schematic of the circulation associated with Langmuir circulation cells. [Fig. 3.26c of Open University Course Team (1989). Reproduced with permission of Butterworth-Heinemann Ltd.]

of regions of convergence within long circulation rolls aligned with the wind direction, as illustrated schematically in Fig. 2.30. This circulation system -called Langmuir circulation - was first studied extensively by Irving Langmuir in 1938, when he observed long rows of seaweed arranged parallel to the wind in the North Atlantic Ocean.

Various theories have been developed to explain the continuance of established rolls through reinforcement of the convergence by the wave field. The origin of the circulation cell is not well understood. It is believed to be the result of an instability in the Ekman spiral, producing variation in the vertical shear; hence the circulation penetrates to the bottom of the mixed layer. The atmosphere also shows such behaviour, although on a larger spatial and temporal scale. Analogous cloud streets, often seen in clear cold air following the passage of a cold front, require hours to form, rather than the 20-30 minutes for Langmuir circulation development.

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  • haris
    What is a langmuir spiral and how does it move Lake water?
    3 years ago

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