 Rayleigh–Taylor instability

Rayleigh-Taylor instability occurs when the effective acceleration places a denser fluid above a lighter one so that small interface disturbances can release gravitational potential energy. A downward bulge of dense fluid tends to sink while adjacent lighter fluid rises. The inertia of the moving fluids determines how rapidly the disturbance grows.

For two deep inviscid incompressible fluids at rest, with upper mass density ${\rho }_h>{\rho }_l$ and no surface tension, a sinusoidal disturbance of horizontal wavenumber $k$ has growth rateIncluding constant surface tension $\gamma$ subtracts $\gamma k^3/({\rho }_h+{\rho }_l)$ from the right-hand side, stabilizing sufficiently short wavelengths.^[ref] The assumptions exclude finite-depth boundaries, viscosity and diffuse interfaces. An idealized two-layer experiment records the interface height after a small imposed disturbance; its early exponential growth can test the linear prediction before the interface rolls into large plumes.

Rayleigh–Taylor instability is a phenomenon in fluid dynamics that occurs at the interface between two fluids of different densities when the lighter fluid is positioned above the heavier fluid. This instability can arise in various physical scenarios, such as in astrophysics, oceanography, and engineering applications. The classic example is a scenario where a heavy fluid (e.g., water) is at rest below a lighter fluid (e.g., oil).