A property of the Rayleigh-Taylor instability

Summary form only given. In his classic paper, Taylor [1] considered the instability on the surfaces of a fluid slab of a finite thickness that is accelerated by a much lighter fluid on either side of the fluid slab. The maximum number of e-foldings in the amplitude growth of the Taylor instability of this fluid slab is given by sqrt(2ks), where k is the wavenumber of the interface perturbation, and s is the distance traveled by the accelerated fluid slab, according to the linear theory. We show that this bound is independent of the magnitude and sign of the acceleration, of the magnitude and sign of the initial velocity of the slab, and of the width of the fluid slab. The primary dependence on the accelerated distance is illustrated in the resistive MHD radiation-hydrodynamics code, HYDRA [2], in which an aluminum slab with an initial sinusoidal surface ripple is accelerated by an intense magnetic pressure. Despite the nine times increase in magnetic pressure (from B = 200 T to 600 T), there is little difference in the Rayleigh-Taylor instability growth after the slab is accelerated for the same distance. This insensitivity to B appears to be the case in the simulation with or without the stabilization effect of the magnetic tension.