Rayleigh–Taylor eigenmodes of a thin layer in the nonlinear regime

In the long-wavelength limit, many aspects of the Rayleigh–Taylor (RT) instability of accelerated fluid shells can be explored by using the thin sheet approximation. For two-dimensional (2-D) planar eigenmodes, analytic nonlinear solutions [E. Ott, Phys. Rev. Lett. 29, 1429 (1972)] are available. Comparing the simplest of them for the nonconstant acceleration, g∝t−2, with Ott’s solution for constant g, the applicability of nonlinear results obtained for constant g to situations with variable acceleration is analyzed. Nonlinear three-dimensional (3-D) effects are investigated by comparing the numerical solutions for axisymmetric Bessel eigenmodes with Ott’s solution for 2-D modes. It is shown that there is a qualitative difference between 2-D and 3-D bubbles in the way they rupture a RT unstable fluid shell: In contrast to the exponential thinning of 2-D bubbles, mass is fully eroded from the top of an axisymmetric 3-D bubble within a finite time of (1.1–1.2)γ−1 after the onset of the free-fall stage; γ is the RT growth rate.