Zonal wavenumber

Short description: Quantity associated with atmospheric waves

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500mb geopotential height averaged between October 9–21, 2010 illustrating Rossby wave pattern with the zonal wavenumber 4. DOE AMIP reanalysis data.

In meteorological applications, a zonal wavenumber or hemispheric wavenumber is the dimensionless number of wavelengths fitting within a full circle around the globe at a given latitude:[1]

k=2πrcos⁡φλ,

where λ is the wavelength, r = 6378 km is the Earth's radius, and φ is the latitude.

Zonal wavenumbers are typically counted on the upper level (say 500-millibar) geopotential maps by identifying troughs and ridges of the waves. Wavenumber 1 has one trough and one ridge, i.e. one wavelength fits 2π = 360°. Wavenumber 2 has two ridges and two troughs around 360°.

Wavenumber 0 corresponds to zonal (symmetric) flow. Wavenumbers 1–3 are called long waves and are often synonymous in meteorological literature with the mid-latitude planetary Rossby waves, while wavenumbers 4–10 are often referred to as "synoptic" waves.[2] In the Northern Hemisphere, wavenumbers 1 and 2 are important for the time-mean circulation due to topography (Tibetan Plateau and Rocky Mountains),[3][4] whereas in the Southern Hemisphere, tropical convection is responsible for the presence of mainly zonal wavenumber 3.[5]

## See also

* Wavenumber

## References

1. ↑ "AMS Glossary". 2015-07-28. http://glossary.ametsoc.org/wiki/Main_Page.
2. ↑ Vallis, Geoffrey K (2006). Atmospheric and Oceanic Fluid Dynamics - Fundamentals and Large-scale Circulation. Cambridge, UK: Cambridge University Press. ISBN 9780521849692.
3. ↑ Held, I; Ting, M; Wang, H (2002). "Northern winter stationary waves: Theory and modeling". Journal of Climate 15 (16): 2125–2144. doi:10.1175/1520-0442(2002)015<2125:NWSWTA>2.0.CO;2. Bibcode: 2002JCli...15.2125H.
4. ↑ Garfinkel, C; White, I; Gerber, E; Jucker, M; Erez, M (2020). "The building blocks of Northern Hemisphere wintertime stationary waves". Journal of Climate 33 (13): 5611–5633. doi:10.1175/JCLI-D-19-0181.1. Bibcode: 2020JCli...33.5611G.
5. ↑ Goyal, Rishav; Jucker, Martin; Sen Gupta, Alex; Hendon, Harry; England, Matthew (2021). "Zonal wave 3 pattern in the Southern Hemisphere generated by tropical convection". Nature Geoscience 14 (10): 732–738. doi:10.1038/s41561-021-00811-3. Bibcode: 2021NatGe..14..732G. http://dx.doi.org/10.1038/s41561-021-00811-3.

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