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.