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# Rossby wave

Rossby (or planetary) waves are large-scale motions in the ocean or atmosphere whose restoring force is the variation in Coriolis effect with latitude. The waves were first identified in the atmosphere in the 1939 by Carl-Gustaf Arvid Rossby who went on to explain their motion.

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## Terrestrial waves

The direction of rotation of the Earth entails that such wave crests always travel East to West. However, the energy associated with the waves can propagate in any direction. In general: shorter waves propagate energy to the east; longer waves propagate energy to the west.

## Atmospheric waves

Rossby waves in the atmosphere are easy to observe as large-scale meanders of the jet stream. When these loops become very pronounced, they detach the masses of cold, or warm, air that become cyclones and anticyclones and are responsible for day-to-day weather patterns at mid-latitudes.

The wave speed is given by:

$c = u - \frac{\beta}{k^2}$

Where c is the wave speed, u is the mean westerly flow, β is the Rossby parameter, and k is the total wavenumber.

## Oceanic waves

In the oceans, Rossby waves are responsible for the asymmetry of circulatory vortices in which the Western arm of a vortex is narrower and flows more rapidly than the Eastern. This western intensification is the effect that drives the Gulf Stream. It was elucidated by Henry M. Stommel who termed it the beta effect .

Rossby waves are generated by atmospheric forcing from winds and buoyancy effects from solar heating and are the principle means by which localised climatic effects drive the global response of the ocean. Waves propagate at only a few centimetres per second, have wavelengths of up to hundreds of kilometres and result in only a few centimetres elevation at the sea surface. However, their passage can result in displacements of the thermocline of the order of many metres.

## Bibliography

• Rossby, C-G (1939), Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permament centers of action, J. Marine Resarch pp38-55
• Platzman, G (1968) The Rossby wave, Quart. J. Roy. Meteorol. Soc. pp94-248
• Dickinson, R E (1978) Rossby waves - long-period oscillations of oceans and atmospheres, Ann. Rev. Fluid Mech. pp10-195