DEFINITION:

The frequency at which an air parcel will oscillate when subjected to an infinitesimal perturbation in a stably stratified atmosphere (Durran and Klemp, JAS 1982).

In unsaturated air the B-V Frequency can be calculated from either

N^2 = (g/T)(dT/dz + X{d})

or

N^2 = g(d ln(theta)/dz)

where T=sensible temperature, theta=potential temperature, X{d}= the dry adiabatic lapse rate and g=gravitational acceleration.

If the air is saturated, there will also be condensation and latent heating upon upward displacement. The result is that the buoyancy resotring force will be diminished and N^2 will be lower in a saturated atmosphere.

To calculate an approximation for the B-V Frequency in a saturated atmosphere one can use the following: (from Durran and Klemp, JAS 1982)

N^2 = g[ X * Y - Z ]

X=(1+(Lq{s}/RT))/(1+(eL^2q{s}/c{p}RT^2))

Y=(dln(theta)/dz)+(L/c{p}T)*(dq{s}/dz)

Z=dq{w}/dz

where q{s}=saturation mixing ratio, L=latent heat of vaporization, R=ideal gas constant for dry air, R{v}=gas constant for water vapor, e=R/R{v}, and c{p}=heat capacity of dry air. See above for descriptions of other variables.