Rossby waves

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Rossby waves Carl-Gustav Rossby (1898–1957) was a Swedish meteorologist who worked for much of his life in the USA. In the 1930s he proposed many of the theoretical ideas which led to an understanding of the large-scale dynamics of the atmosphere.

Imagine flying in a balloon at a height of about 10km in the atmosphere. The balloon would be carried along by the wind at that level. If the site from which the balloon was launched was at 50°N, then the balloon would normally be blown from west to east, since that is the prevailing wind direction at that latitude and height. However, the balloon would not move round the Earth at exactly 50° latitude but would meander north and south of this latitude for long periods of time. It is as if the balloon were caught in waves which at some places would tend to move it southward for a while and would then later move it northward. As the balloon moved round the Earth, eventually returning to approximately where it started, it might have moved south and north about two or three or four times on these waves. The waves are enormous, each one spanning perhaps 5000 to 10 000km. An even more surprising aspect of these waves is that they are almost stationary. We expect waves, for example those at the sea shore, to be moving, but it is also possible for the wave pattern to be stationary although air is moving through the waves and a balloon carried by the air would follow the wave pattern. If our hypothetical balloon were to begin a second journey round the Earth, and the waves were exactly stationary, then the balloon would follow the same wave pattern at the same locations above the Earth.

Rossby was able to give a simple and elegant explanation for these waves, which had been observed in the atmosphere. Under certain simplifying assumptions it is possible to assume that the absolute vorticity (a combination of the spin of the air and the spin of the Earth) is conserved, that is, it will not change over a period of time. As air moves towards the poles the contribution from the Earth's spin increases. If the sum of the air's vorticity (known as the relative vorticity, since it is measured relative to the Earth) and the Earth vorticity is to remain constant, then the vorticity of the air must decrease. This causes it to turn away from the pole and move southward. The reverse process operates as the air moves towards the Equator; so it turns poleward again. Since this motion is superimposed on a general west-to-east motion, the air moves through a wave-like pattern.

More recently the theoretical understanding of these waves has been taken much further by removing some of Rossby's original simplifying assumptions and extending the waves to three dimensions so that their vertical structure and motion can be explained. These more complex waves have, however, retained the name ‘Rossby waves’. Our understanding of the structure of Rossby waves has been valuable in explaining some observed climatological patterns which show that some regions of the world tend to be warm when others are cold, or that some parts are dry when others are wet.

Charles N. Duncan

Bibliography

Holton, J. R. (1979) An introduction to dynamical meteorology. Academic Press, London.

Rossby waves Named after the Swedish-American meteorologist C. -G. Rossby (1898–1957), Rossby waves are equatorward troughs and poleward ridges forming long waves in the circumpolar flow of the upper air, particularly in the mid and upper troposphere, with a typical wavelength of around 2000 km. Three or four waves usually occur in the circumpolar westerly wind flow over mid latitudes. They may remain stationary (as standing waves) when wind speed and wavelength have a given relationship. The waves may be initiated by lower winds over mountain barriers, e.g. the Rocky Mountains, or by heating over warm oceans in winter or over land in summer. They are then amplified by vorticity (due to the Earth's rotation) in anticyclonic curvature (in ridges) and in cyclonic curvature (in troughs). Characteristic positions for the main troughs in the upper westerlies over the northern hemisphere are about 70° W and 150° E. The Rossby waves influence the formation of surface depressions which tend to develop on a frontal wave ahead of an upper trough. Rossby waves also occur in the oceans.

Rossby waves Troughs extending towards the equator and ridges extending towards the poles that form long waves in the circumpolar flow of the upper air, particularly in the mid and upper troposphere, with a typical wavelength of around 2000 km; in the northern hemisphere the main troughs are characteristically at about 70°W and 150°E and three or four waves usually occur in the circumpolar westerly wind flow over mid-latitudes. The Rossby waves influence the formation of surface depressions which tend to develop on a frontal wave ahead of an upper trough. They are named after the Swedish-American meteorologist C. G. Rossby (1898–1957).