### Brunt-Väisälä frequency

(buoyancy frequency)
(natural frequency of buoyancy waves)

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. It is defined as:

```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).

(Often the equation is given in terms of a temperature rather than density: I presume this is because of the relationship between them if the ideal gas law holds.) 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.

(atmosphere,fluid dynamics)