On a sphere, the integer counts complete zonal oscillations around a latitude circle. Its local Cartesian wavenumber at latitude is for radius . The integer and the dimensional local wavenumber should not be interchanged in a local dispersion relation for Rossby waves.
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Zonal wavenumber is a term used in atmospheric science and oceanography to describe the spatial frequency of wave patterns in a zonal (east-west) direction in a periodic system, like the Earth's atmosphere or ocean. It quantifies how many wavelengths fit into a given distance in the zonal direction.