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In meteorological applications, a zonal wavenumber or hemispheric wavenumber is the
In meteorological applications, a zonal wavenumber or hemispheric wavenumber is the dimensionless number
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
of wavelengths fitting within a full circle around the globe at a given latitude.
:
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
The bar is a metric unit of pressure, but not part of the International System of Units (SI). It is defined as exactly equal to 100,000 Pa (100 kPa), or slightly less than the current average atmospheric pressure on Earth at sea leve ...
) geopotential
Geopotential is the potential of the Earth's gravity field. For convenience it is often defined as the ''negative'' of the potential energy per unit mass, so that the gravity vector is obtained as the gradient of this potential, without the negat ...
maps by identifying troughs and ridges
A ridge or a mountain ridge is a geographical feature consisting of a chain of mountains or hills that form a continuous elevated crest for an extended distance. The sides of the ridge slope away from the narrow top on either side. The line ...
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
Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids. They were first identified by Sweden-born American meteorologist Carl-Gustaf Arvid Rossby. They are observed in the atmospheres and ...
, while wavenumbers 4-10 are often referred to as "synoptic" waves. In the Northern Hemisphere, wavenumbers 1 and 2 are important for the time-mean circulation due to topography (Tibetan Plateau
The Tibetan Plateau (, also known as the Qinghai–Tibet Plateau or the Qing–Zang Plateau () or as the Himalayan Plateau in India, is a vast elevated plateau located at the intersection of Central, South and East Asia covering most of the ...
and Rocky Mountains
The Rocky Mountains, also known as the Rockies, are a major mountain range and the largest mountain system in North America. The Rocky Mountains stretch in straight-line distance from the northernmost part of western Canada, to New Mexico ...
), whereas in the Southern Hemisphere, tropical convection is responsible for the presence of mainly zonal wavenumber 3.
See also
*Wavenumber
In the physical sciences, the wavenumber (also wave number or repetency) is the '' spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to te ...
References
{{DEFAULTSORT:Zonal wavenumber Atmospheric dynamics Rates