Stratified Buoyancy Frequency

Displace a fluid parcel to reveal oscillatory, neutral or overturning stratification. By examining the vertical density gradient in an incompressible Boussinesq fluid, we can characterize its stability and the restoring or driving forces when a parcel is displaced from its equilibrium position.

Experiment

You can interact with these dynamics directly using the Stratified Buoyancy Frequency module.

1. Set the "Density gradient" control to -2. This creates a stable stratification where density decreases with height (a negative gradient when z points upwards).
2. Set the "Displacement" to 0.5 m to give the parcel an initial offset from its equilibrium depth.
3. Change the "Time" control to 5 s. Observe the calculated "Parcel displacement" which should match approximately 0.382 m.
4. Now change the "Density gradient" to 2 kg/m⁴. The value of N² becomes negative (-0.01962), indicating an unstable (overturning) stratification. The stability changes to "Unstable".
5. At t = 5 s in this unstable regime, note that the displacement grows rather than oscillates (0.627 m), and the acceleration is positive, driving the parcel further away from z=0.