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]
where λ is the wavelength, r 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 degrees. Wavenumber 2 has two ridges and two troughs around 360 degrees.
Wavenumber 0 corresponds to zonal (symmetric) flow. Wavenumbers 1–3 are called long waves and 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]
^Vallis, Geoffrey K (2006). Atmospheric and Oceanic Fluid Dynamics - Fundamentals and Large-scale Circulation. Cambridge, UK: Cambridge University Press.
ISBN9780521849692.