Look at this buoyancy experiment. Forcing an inverted immiscible oil layer to suspend by applying a vibration to an injected air layer underneath this layer. This vibration prevents a Rayleigh–Taylor instability (i.e. glob dripping) from collapsing the layer.


from this article: [Floating under a levitating liquid](https://www.nature.com/articles/s41586-020-2643-8)

Have to look at the liquid stabilization more closely -- the formulation looks close to a Mathieu equation. This has long been used to describe sloshing in a liquid amongst other behaviors. From the [supplementary doc](https://static-content.springer.com/esm/art%3A10.1038%2Fs41586-020-2643-8/MediaObjects/41586_2020_2643_MOESM1_ESM.pdf)


[Mathieu equation](https://en.wikipedia.org/wiki/Mathieu_function)

\\( {\displaystyle {\frac {d^{2}y}{dt^{2}}}+(a-2q\cos 2t)y=0,} \\)

The solution to the Mathieu equation (Mathieu function) is known to have stable & unstable regimes for specific parameters, which reveals as a harmonic-rich spectrum. With the sustained forcing the Rayleigh–Taylor instability is restricted to these ordered harmonics, thus preventing collapse?