Viscous and elastic Rayleigh–Taylor instability at a dynamic interface in cylindrical geometry

In this paper, we apply the potential flow theory to study the Rayleigh–Taylor instability at an imploding interface associated with the Bell–Plesset effects in the cylindrical geometry. The coupled equations to describe the motion of the interface are numerically solved to understand how the physical properties of the external medium and the driving pressure affect its instability. Generally, the viscosity inhibits the interfacial motion. With higher viscosity, namely, smaller Re, the acceleration of interfacial motion is particularly inhibited, while the radius and velocity is slightly suppressed, leading to the amplitude for all modes being slowed down uniformly. On the contrary, the radius possesses pure oscillations with the presence of elasticity. For the perturbed amplitudes in the linear regime, the larger modes are accompanied by the higher frequency of oscillation but the smaller amplitude. In addition, there is a single mode that excites the largest perturbation in the elastic phase, and the perturbation is significantly suppressed when the mode is sufficiently large. Smaller values of driven pressure cause the faster rate of decay, and the perturbation will be more easily suppressed at the lower modes. When the pressure is large enough, the perturbation grows rapidly with increasing modes and is difficult to be suppressed. The above conclusions provide a deeper understanding of the mechanistic interactions between material properties and dynamic stability in high energy density physics.