# Brunt-Väisälä frequency

In

atmospheric dynamics ,oceanography , andgeophysics , the**Brunt-Väisälä frequency**, orbuoyancy frequency, is the frequency at which a vertically displaced parcel will oscillate within a statically stable environment. In the atmosphere,: $N\; equiv\; sqrt\{frac\{g\}\{\; heta\}frac\{d\; heta\}\{dz$, where $heta$ is

potential temperature , $g$ is the local acceleration ofgravity , and $z$ isgeometric height .In the ocean where

salinity is important, or in fresh water lakes near freezing, where density is not a linear function of temperature,: $N\; equiv\; sqrt\{-frac\{g\}\{\; ho\}frac\{d\; ho\}\{dz$, where $ho$, 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 backgroundstratification (in which the density changes in the vertical). The parcel, perturbed vertically from itsstarting position, experiences a vertical acceleration. If the acceleration is back towards the initialposition, the stratification is said to be stable and the parcel oscillates vertically. In this case, N

^{2}>0 and the frequency of oscillation is given by N. If the acceleration is away from the initial position (N^{2}<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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