The three-dimensional weakly nonlinear Rayleigh–Taylor instability in spherical geometry

Abstract

The fully three-dimensional Rayleigh–Taylor instability in spherical geometry is investigated in the weakly nonlinear regime. A theoretical model is developed for incompressible fluid and ideal Euler equations. Third-order solutions are derived for interface perturbations of spherical harmonic modes, Yn,m. Interface evolution, fundamental mode growth, the generated spectrum, and bubble growth are determined. It is found that the fastest growing modes satisfy the relation m≃(n+1)/2. The generated spectra demonstrate the feedback of mode coupling, which greatly depends on the azimuthal mode numbers. The growth factors are nearly the same for bubbles at different latitudes and bubbles with initially round cross-sectional perturbation shapes grow faster.