Effect of initial phase on the Rayleigh–Taylor instability of a finite-thickness fluid shell

Rayleigh–Taylor instability(RTI) of finite-thickness shell plays an important role in deep understanding the characteristics of shell deformation and material mixing. The RTI of a finite-thickness fluid layer is studied analytically considering an arbitrary perturbation phase difference on the two interfaces of the shell. The third-order weakly nonlinear(WN) solutions for RTI are derived. It is found the main feature(bubble-spike structure) of the interface is not affected by phase difference. However, the positions of bubble and spike are sensitive to the initial phase difference, especially for a thin shell(kd < 1), which will be detrimental to the integrity of the shell. Furthermore, the larger phase difference results in much more serious RTI growth, significant shell deformation can be obtained in the WN stage for perturbations with large phase difference. Therefore, it should be considered in applications where the interface coupling and perturbation phase effects are important, such as inertial confinement fusion.