Brunt–Väisälä frequency

In atmospheric dynamics, oceanography, asteroseismology and geophysics, the Brunt–Väisälä frequency, or buoyancy frequency, is the angular frequency at which a vertically displaced parcel will oscillate within a statically stable environment. It is named after David Brunt and Vilho Väisälä. It can be used as a measure of atmospheric stratification.

Consider a parcel of (water or gas) that has density of ${\displaystyle \rho _{0}}$ and the environment with a density that is a function of height: ${\displaystyle \rho =\rho (z)}$. If the parcel is displaced by a small vertical increment ${\displaystyle z'}$, it will be subject to an extra gravitational force against its surroundings of:

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