Nonlinear, single-mode, two-dimensional Rayleigh-Taylor instability in ideal media

A model for the single mode, two-dimensional Rayleigh-Taylor instability in ideal, incompressible, immiscible, and inviscid fluids is developed as an extension of a previous linear model based on the Newton's second law [A. R. Piriz et al., Am. J. Phys. 74, 1095 (2006)0002-950510.1119/1.2358158]. It describes the transition from linear to nonlinear regimes and takes into account the mass of fluids participating in the motion during the instability evolution, including the laterally displaced mass. This latter feature naturally leads to the bubble and spike velocity saturation without requiring the usual drag term necessary in the well-known buoyancy-drag model (BDM). In addition, it also provides an explanation to the latter phase of bubble reacceleration without appealing to the vorticity generation due to the Kelvin-Helmholtz instability. The model is in perfect agreement with the BDM buoyancy-drag model, but, apart from extending its range of application, it solves many of its issues of concern and provides a more consistent physical picture.