Linear and nonlinear Rayleigh-Taylor growth at strongly convergent spherical interfaces

Abstract

Recent attention has focused on the effect of spherical convergence on the nonlinear phase of Rayleigh-Taylor growth. For instability growth on spherically converging interfaces, modifications to the predictions of the Layzer model for the secular growth of a single, nonlinear mode have been reported [D. S. Clark and M. Tabak, Phys. Rev. E 72, 0056308 (2005).]. However, this model is limited in assuming a self-similar background implosion history as well as only addressing growth from a perturbation of already nonlinearly large amplitude. Additionally, only the case of singlemode growth was considered and not the multimode growth of interest in applications. Here, these deficiencies are remedied. First, the connection of the recent nonlinear results including convergence to the well-known results for the linear regime of growth is demonstrated. Second, the applicability of the model to more general implosion histories (i.e., not self-similar) is shown. Finally, to address the case of multimode growth with convergence, the recent nonlinear single mode results are combined with the Haan model formulation for weakly nonlinear multimode growth. Remarkably, convergence in the nonlinear regime is found not to modify substantially the multimode predictions of Haan's original model.