Zonal wavenumber

Zonal wavenumber is the integer number of complete sinusoidal cycles of a Rossby wave that fit around a latitude circle of the Earth. It is the fundamental spatial frequency of planetary-scale atmospheric motions, determining how many high-pressure and low-pressure ridges and troughs encircle the globe at a given latitude. Zonal wavenumber 1 describes a single planetary wave — a massive hemispheric meander — while wavenumber 6 or 7 describes the familiar pattern of mid-latitude storm systems.

The wavenumber is not merely descriptive; it determines the wave's phase speed, group velocity, and its capacity for wave-mean flow interaction. Low wavenumbers propagate slowly westward and are most susceptible to amplification and blocking, while high wavenumbers travel rapidly eastward with the jet stream. The observed preference of the atmosphere for wavenumbers 5–7 in mid-latitudes is itself a puzzle: why does the climate system select these scales rather than others? The answer likely involves the interaction of the Earth's radius, rotation rate, and meridional temperature gradient — a scale selection problem that remains incompletely solved.