Zonal wavenumber
{{Short description|Quantity associated with atmospheric waves}}
{{One source|date=December 2016}}
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:{{cite web|url=http://glossary.ametsoc.org/wiki/Main_Page |title=AMS Glossary |website=Glossary.ametsoc.org |date=2015-07-28 |access-date=2016-12-01}}
:
where λ is the wavelength, r = 6378 km is the Earth's radius, and 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.{{cite book |last1=Vallis |first1=Geoffrey K |title=Atmospheric and Oceanic Fluid Dynamics - Fundamentals and Large-scale Circulation |date=2006 |publisher=Cambridge University Press |location=Cambridge, UK |isbn=9780521849692}} In the Northern Hemisphere, wavenumbers 1 and 2 are important for the time-mean circulation due to topography (Tibetan Plateau and Rocky Mountains),{{cite journal |last1=Held |first1=I |last2=Ting |first2=M |last3=Wang |first3=H |title=Northern winter stationary waves: Theory and modeling |journal=Journal of Climate |date=2002 |volume=15 |issue=16 |pages=2125–2144 |doi=10.1175/1520-0442(2002)015<2125:NWSWTA>2.0.CO;2|doi-access=free |bibcode=2002JCli...15.2125H }}{{cite journal |last1=Garfinkel |first1=C |last2=White |first2=I |last3=Gerber |first3=E |last4=Jucker |first4=M |last5=Erez |first5=M |title=The building blocks of Northern Hemisphere wintertime stationary waves |journal=Journal of Climate |date=2020 |volume=33 |issue=13 |pages=5611–5633 |doi=10.1175/JCLI-D-19-0181.1|s2cid=214141950 |doi-access=free |bibcode=2020JCli...33.5611G |hdl=1959.4/unsworks_66873 |hdl-access=free }} whereas in the Southern Hemisphere, tropical convection is responsible for the presence of mainly zonal wavenumber 3.{{cite journal |last1=Goyal |first1=Rishav |last2=Jucker |first2=Martin |last3=Sen Gupta |first3=Alex |last4=Hendon |first4=Harry |last5=England |first5=Matthew |title=Zonal wave 3 pattern in the Southern Hemisphere generated by tropical convection |journal=Nature Geoscience |date=2021 |volume=14 |issue=10 |pages=732–738 |doi=10.1038/s41561-021-00811-3 |bibcode=2021NatGe..14..732G |s2cid=237310074 |url=http://dx.doi.org/10.1038/s41561-021-00811-3|hdl=1959.4/unsworks_79009 |hdl-access=free }}