The Rayleigh-Taylor instability occurs when a heavy fluid is supported by a lighter fluid. It controls astrophysical, geophysical, and industrial processes such as supernova explosions, the formation of salt domes, and the implosion of inertial-confinement-fusion capsules.
The linear regime is well understood. The nonlinear regime is usually treated by numerical simulations or high-order expansion of the fluid equations. The purpose of this talk is to present a time evolution equation for Rayleigh-Taylor instability from the linear to the nonlinear regime and give analytic solution for the nonlinear regime. It is found that the Rayleigh-Taylor instability grows from the exponential growth to the algebraic growth due to the quasilinear modification of the equilibrium density. The nonlinear growth becomes weaker as the wave length is longer than the density gradient scale.