Bell–Plesset effects on Rayleigh–Taylor instability at cylindrically divergent interfaces between viscous fluids

Abstract

We report the first experiments on divergent Rayleigh–Taylor instability (RTI) at well-controlled single-mode cylindrical interfaces between air and viscous liquid. At early stages, only the amplitude of the dominant single mode grows with time while the higher harmonics starts to grow in the late stage. The transition point from the linear stage to the nonlinear stage is defined as the moment when the higher harmonics starts to grow and the linear stage before the Poiseuille flow fully developed is concerned in this paper. We find that the growth rate is lower than that in convergent or planar geometry due to geometric divergence. Both divergent Bell–Plesset (BP) effects and viscosity effect inhibit the growth rate of RTI. The attenuation strength of viscosity effect is reduced by divergent BP effects compared with the planar case. It is observed that the value ka ∼ (0.188–0.314), at the transition point, is much lower than that in planar geometry (ka ∼ 1), where a is the amplitude of the dominant single mode and k is the initial wavenumber. To take viscosity into account, a new approximate model based on the Bell theory is proposed, which well predicts the perturbation growth in a divergent geometry in the linear stage before the Poiseuille flow fully developed.