Dependence of Rayleigh–Taylor instability of finite-thickness shell on initial perturbed wavelengths

Rayleigh–Taylor instability (RTI) of finite-thickness shell significantly impacts shell deformation and material mixing processes, with crucial implications for inertial confinement fusion (ICF). This study focuses on the RTI growth at the dual interfaces of a thin shell. A second-order weakly nonlinear (WN) analytical theory is developed to investigate the nonlinear deformation of the shell induced by different perturbation wavelengths initially imposed at the upper and lower interfaces. The validity of the theoretical results within the WN regime has been confirmed via two-dimensional Eulerian numerical simulations. Due to the interface coupling effect, the initially imposed single-mode perturbations at the upper and lower interfaces progressively evolve, exhibiting characteristics typical of multi-mode perturbations. When the initial perturbation wavelengths differ significantly, the primary structure of RTI retains its integrity, a behavior attributed to the dominance of long-wavelength perturbations. For comparable initial wavelengths, mode-coupling significantly distorts the bubble-spike structure in RTI, with the thin shell becoming prone to rupture due to enhanced nonlinear interactions.