Rossby and Kelvin waves

If William Thomson, better known as Lord Kelvin, born in Belfast in 1824, is famous for introducing the “absolute zero” of the temperature scale corresponding to the absolute absence of thermal agitation, this British physicist is not less renowned for his work in fluid dynamics. Kelvin conceptualized in 1879 the existence of an ocean wave that results from both the Coriolis force due to the rotation of the Earth and the reaction against a topographic boundary such as a coastline. The Kelvin wave also has the property of being trapped along the equator, due to the vanishing of the Coriolis force, and propagates eastward. This same phenomenon occurs in the atmosphere.

A very important characteristic of a Kelvin wave is that it is non-dispersive[i], i.e. its phase velocity c is constant, whatever the wavelength: it varies between 2.3 m/s and 2.8 m/s for the first baroclinic mode, depending on the oceans. In a stratified ocean, the various baroclinic modes result in the oscillation at the interfaces of layers of different densities, producing waves whose phase velocity decreases with the depth of the interface: the maximum speed corresponds to the first baroclinic mode, i.e. the oscillation of the thermocline.

Carl-Gustaf Arvid Rossby born in Stockholm in 1898, a Swedish meteorologist then naturalized American, was the first to explain the large scale motions of the atmosphere through the fluid mechanics. In the 20’s, he studied hydrodynamics, the general circulation of the oceans and the atmosphere. As Rossby waves are easy to observe in the atmosphere because they form large-scale meanders of the jet-stream in mid-latitudes, ocean waves have been observed at the advent of satellite oceanography, although conceptualized as early as 30’s. Also known as planetary waves as they owe their origin to the shape and rotation of the earth, it is the crucial difference between the horizontal scale (of the order of hundreds or even thousands of kilometers) and vertical (a few centimeters) of these waves that makes them so difficult to observe. In addition, very often they take the form of solitary waves (with one peak or one trough).

Another important feature is that Rossby waves are trapped by the equator, but unlike Kelvin waves, they propagate westward or cyclonically along the subtropical gyres. Their propagation speed of a few m/s, decreases as the latitude increases. This means that at mid-latitudes the wave can take months – even years – to cross the Pacific Ocean. The solutions of the equations of motion of Rossby waves at low frequencies and long wavelengths are non-dispersive, hence the propensity of these waves to cross the oceans without distortion.


[i] Non-dispersive waves

They are such that the phase velocity of the ridge of the wave is equal to the group velocity of the energy carried by the wave, and this for all the frequencies (or all wavelengths). This means that the wave propagates without deformation.

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