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The nonlinear growth of perturbations in hydrodynamic interfacial instabilities can be of particular importance in both scientific research (e.g. supernova explosion) and engineering applications (e.g. inertial confinement fusion). One of the most significant issues in these instabilities is the long-time nonlinear bubble evolution of a single-mode Rayleigh–Taylor instability (RTI), which remains as an unsolved and challenging problem since Taylor’s seminal work more than seven decades ago. Introduced in this paper is an analytical model for the long-time evolution of bubble velocity, curvature and vorticity, which is established by considering the vorticity accumulation around the bubble in a bilaterally rotational flow system under the classical planar potential-flow theory framework. The proposed theoretical model incorporates not only the classical linear, nonlinear and quasi-steady stages, but the late re-acceleration stage. Meanwhile, the new model can capture the phenomenon of secondary velocity saturation following the stage of bubble re-acceleration. The good agreement between the present model and numerical simulations for all density ratios and dimensions confirms that the accumulation in vorticity tends to break the early stage buoyancy-drag equilibrium mechanism and leads to the establishment of a new equilibrium in the late-stage RTI.
Liu et al. (Wed,) studied this question.