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The Brunt-Väisälä frequency (or buoyancy frequency) is a characteristic frequency of buoyancy waves in a stratified fluid, specifically the frequency of the oscillation caused by a vertical displacement of a parcel of fluid within a still body of fluid whose density varies with depth, lying stably within a gravitational field. The concept is used in meteorology and other sciences and applies to stars and planet atmospheres. This is the frequency of oscillations that form if there is a disturbance, and example being air pushed over a the top of mountain, and wavering up and down a bit even after it is passing over flat land again. A version for simple cases is:
N² = -(g/ρ0) ∂ρ/∂z
There are variants for specific types of cases.