On the Bell–Plesset effects: The effects of uniform compression and geometrical convergence on the classical Rayleigh–Taylor instability

Abstract

The Rayleigh–Taylor (RT) instability of an accelerating fluid interface is examined considering the effects of compression and geometrical convergence on incompressible perturbations of an interface separating two homogeneous compressible fluid layers of different mass densities. These effects occur in the implosion of inertial confinement fusion capsules. A complete description of Bell–Plesset effects is presented in terms of a simple model formulated in terms of the mass amplitude of perturbations of planar, cylindrical, and spherical interfaces. This formulation makes a clear distinction between perturbation growth driven by buoyant force—the RT instability—and modifications of perturbation behavior by compression and geometrical convergence—the Bell–Plesset (BP) effects [G. I. Bell, Los Alamos National Laboratory, Report LA-1321 (1951); M. S. Plesset, J. Appl. Phys. 25, 96 (1954)]. BP effects modify RT growth rates and may affect RT stability criteria, but they are not a distinct instability. These effects vary widely in their nature and importance from application to application, depending on the relative rates of RT growth, radial convergence, and uniform compression. Limiting cases are compared and contrasted. BP effects are generally different for each component of the perturbation solution pair. BP effects on perturbation growth in cylindrical implosion experiments have been analyzed successfully [e.g., W. W. Hsing et al., Phys. Plasmas 4, 1832 (1997)], in terms of an incomplete single-component solution that is indistinguishable from unperturbed flow, indicating that the component exhibiting true ongoing perturbed motion is largely absent. This static mass perturbation solution is often treated as the one and only BP effect, even though it occurs as one of a pair of solutions and only in the limit of a vanishing RT effect.