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# Brunt-Väisälä frequency

In atmospheric dynamics and oceanography, the Brunt-Väisälä frequency, or buoyancy frequency, is the frequency at which a vertically displaced parcel will oscillate within a statically stable environment. In the atmosphere,

$N \equiv \sqrt{\frac{g}{\theta}\frac{d\theta}{dz}}$, where θ is potential temperature, g is the local acceleration of gravity, and z is geometric height.

### Additional recommended knowledge

In the ocean where salinity is important, or in fresh water lakes near freezing, where density is not a linear function of temperature,

$N \equiv \sqrt{\frac{g}{\rho}\frac{d\rho}{dz}}$, where ρ, the potential density, depends on both temperature and salinity.

## Context

Dynamical processes to which the Brunt frequency apply are adiabatic and embedded in a buoyantly stable, continuously stratified, hydrostatic fluid. Parcels that are vertically perturbed are accelerated back to their initial position by a restoring buoyancy force. The oscillation is caused as a parcel "overshoots" its neutral position and so is accelerated back in the opposite direction.

In a statically unstable environment, vertically displaced fluid parcels do not oscillate, but instead continue to move in the direction of their initial displacement.

The frequency can be used to determine the frequency of internal waves and provides a useful description of atmospheric and oceanic stability; the parcel will oscillate about its equilibrium position with a frequency related to the steepness of the density gradient.