### The Brunt-Väisälä Frequency

The Brunt-Väisälä frequency N [s^{-1}] describes the oscillation frequency of an air parcel in a stable atmosphere.

where θ is the potential temperature in [K], g the gravitational acceleration in [m/s^{2}] and z the height in [m].

**Figure 7:** Buoyancy oscillation with advection. © The COMET Program

In a **stable air mass**, a vertically perturbed air parcel (e.g. by vertical lift in a mountain range) will have the tendency to come back to its initial position because the air parcel cools when lifted and warms up compared to the surrounding air temperature when dragged down. In this case, **N ^{2} > 0** and the oscillation frequency is given by N. In an

**unstable air mass, N**and the vertically perturbed air parcel will move away from its original position instead of returning to it (e.g. convection).

^{2}< 0