Weakly nonlinear Rayleigh–Taylor instability of finite-thickness fluid supported by a semi-infinite fluid

Rayleigh–Taylor instability (RTI) in multi-interface shells significantly influences shell deformation and material mixing, thereby affecting inertial confinement fusion (ICF) implosion performance. This study investigates the weakly nonlinear (WN) RTI in a finite-thickness fluid shell supported by a semi-infinite fluid. We derive the governing equations and third-order WN solutions for RTI growth at both interfaces of the shell. Numerical simulations based on the two-dimensional Eulerian framework confirm the validity of the theoretical results in the WN regime. The perturbation growth rate at the lower interface and the interfacial coupling coefficients both exhibit explicit dependence on the Atwood number A and the normalized shell thickness ξ. The WN growth and the deformation of the shell are investigated through the third-order solutions. Comparisons are made with the classical RTI in the WN regime under different initial conditions. Additionally, we analyze the saturation amplitude of the perturbation fundamental mode. It is found that the Atwood number and finite-thickness effects play a pivotal role in the WN evolution of the fluid layer.