Definitions

# Brunt-Väisälä frequency

In atmospheric dynamics, oceanography, and geophysics, 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,

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

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

$N equiv sqrt\left\{-frac\left\{g\right\}\left\{rho\right\}frac\left\{drho\right\}\left\{dz\right\}\right\}$, where $rho$, the potential density, depends on both temperature and salinity.

## Context

The concept derives from Newton's Second Law when applied to a fluid parcel in the presence of a background stratification (in which the density changes in the vertical). The parcel, perturbed vertically from its starting position, experiences a vertical acceleration. If the acceleration is back towards the initial position, the stratification is said to be stable and the parcel oscillates vertically. In this case, N2>0 and the frequency of oscillation is given by N. If the acceleration is away from the initial position (N2<0), the stratification is unstable. In this case, overturning or convection generally ensues.

The Brunt-Väisälä frequency relates to internal gravity waves and provides a useful description of atmospheric and oceanic stability.

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