Zonal wavenumber explained

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 = (2 \pi r\cos\varphi)/(λ ,) where λ is the wavelength, r = 6378 km is the Earth's radius, and \varphi 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

Notes and References

1. Web site: AMS Glossary . Glossary.ametsoc.org . 2015-07-28 . 2016-12-01.
2. Book: Vallis . Geoffrey K . Atmospheric and Oceanic Fluid Dynamics - Fundamentals and Large-scale Circulation . 2006 . Cambridge University Press . Cambridge, UK . 9780521849692.
3. Held . I . Ting . M . Wang . H . Northern winter stationary waves: Theory and modeling . Journal of Climate . 2002 . 15 . 16 . 2125–2144 . 10.1175/1520-0442(2002)015<2125:NWSWTA>2.0.CO;2. free . 2002JCli...15.2125H .
4. Garfinkel . C . White . I . Gerber . E . Jucker . M . Erez . M . The building blocks of Northern Hemisphere wintertime stationary waves . Journal of Climate . 2020 . 33 . 13 . 5611–5633 . 10.1175/JCLI-D-19-0181.1. 214141950 . free . 2020JCli...33.5611G .
5. Goyal . Rishav . Jucker . Martin . Sen Gupta . Alex . Hendon . Harry . England . Matthew . Zonal wave 3 pattern in the Southern Hemisphere generated by tropical convection . Nature Geoscience . 2021 . 14 . 10 . 732–738 . 10.1038/s41561-021-00811-3 . 2021NatGe..14..732G . 237310074 . 1959.4/unsworks_79009 . free .