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 planetatmospheres.
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
N - Brunt-Väisälä frequency.
z - depth.
ρ - density of the fluid (a function of z).
ρ0 - density at the point of disturbance.
g - gravity acceleration (e.g., 9.8m/s² at Earth's surface).