  We derive interface models for 3D Rayleigh-Taylor instability (RTI), making
use of a novel asymptotic expansion in the non-locality of the fluid flow.
These interface models are derived for the purpose of studying universal
features associated to RTI such as the Froude number in single-mode RTI, the
predicted quadratic growth of the interface amplitude under multi-mode random
perturbations, the optimal (viscous) mixing rates induced by the RTI and the
self-similarity of horizontally averaged density profiles, and the remarkable
stabilization of the mixing layer growth rate which arises for the three-fluid
two-interface heavy-light-heavy configuration, in which the addition of a third
fluid bulk slows the growth of the mixing layer to a linear rate. Our interface
models can capture the formation of small-scale structures induced by severe
interface roll-up, reproduce experimental data in a number of different
regimes, and study the effects of multiple interface interactions even as the
interface separation distance becomes exceedingly small. Compared to
traditional numerical schemes used to study such phenomena, our models provide
a computational speed-up of at least two orders of magnitude.
