  The onset and development of instabilities is one of the central problems in
fluid mechanics. Here we develop a connection between instabilities of free
fluid interfaces and inverted pendula. When acted upon solely by the
gravitational force, the inverted pendulum is unstable. This position can be
stabilised by the Kapitsa phenomenon, in which high-frequency low-amplitude
vertical vibrations of the base creates a fictitious force which opposes the
gravitational force. By transforming the dynamical equations governing a fluid
interface into an appropriate pendulum, we demonstrate how stability can be
induced in fluid systems by properly tuned vibrations. We construct a
"dictionary"-type relationship between various pendula and the classical
Rayleigh-Taylor, Kelvin-Helmholtz, Rayleigh-Plateau and the self-gravitational
instabilities. This makes several results in control theory and dynamical
systems directly applicable to the study of "tunable" fluid instabilities,
where the critical wavelength depends on the external forces or the instability
is suppressed entirely. We suggest some applications and instances of the
effect ranging in scale from microns to the radius of a galaxy.
