Rayleigh–Taylor growth at decelerating interfaces

The Rayleigh–Taylor ~RT! instability is important in a number of research contexts. For the design or analysis of experiments and observations, it is often useful to know the growth exponent of an interface, even when the growth is strongly nonlinear. The growth exponent is defined here as the number of linear e-foldings by which initial perturbations at the interface would be amplified, if they remained in the regime of linear amplification. Even though the interfaces in actual experiments often develop very nonlinear structures, the growth exponent can still be useful, as a characterization of the degree of nonlinearity. Here we are concerned with the calculation of growth exponents, under simple assumptions, at a decelerating interface. Decelerating interfaces are important in any impulsively driven system, including supernovae, stellar eruptions, and laboratory studies of hydrodynamic turbulence. Here we will represent the growth exponent, G , as the integral of the growth rate, g, over time,