Asymptotic bubble evolutions of the Rayleigh–Taylor instability

We examine the multiple harmonic model for the single-mode Rayleigh–Taylor instability, and present a new class of the asymptotic solution for the bubble evolution. Previously reported solutions for the bubble curvature and velocity from the model were quantitatively different from other theoretical models and numerical results, for small density jumps. The discrepancy between the theoretical models is resolved by our new approach to the model. Our solution agrees with the Layzer–Goncharov model, and gives the independence of the bubble curvature on the density ratio.

► We study the multiple harmonic model for the single-mode Rayleigh–Taylor instability, applying a new approach.
► We present a new class of the asymptotic solution for the bubble evolution.
► A discrepancy between theoretical models is resolved by our new approach to the model.
► We find a physical behavior that the velocity fields have small gradients near behind the bubble tip at the nonlinear stage.
► Our solution agrees with numerical results, and gives the independence of the bubble curvature on the density ratio.