Bell-Plesset effects for an accelerating interface with contiguous density gradients

Abstract

A Plesset-type treatment [M. S. Plesset, J. Appl. Phys. 25, 96 (1954)] is used to assess the effects of contiguous density gradients at an accelerating spherical classical interface on Rayleigh-Taylor and Bell-Plesset perturbation growth. Analytic expressions are obtained that describe enhanced Rayleigh-Taylor instability growth from contiguous density gradients aligned with the acceleration and which increase the effective Atwood number of the perturbed interface. A new pathway for geometric amplification of surface perturbations on an accelerating interface with contiguous density gradients is identified. A resonance condition between the density-gradient scale length and the radius of the interface is also predicted based on a linearized analysis of Bernoulli’s equation, potentially leading to enhanced perturbation growth. Comparison of the analytic treatment with detailed two-dimensional single-mode growth-factor simulations shows good agreement for low-mode numbers where the effects of spherical geometry are most manifested.