A theoretical analysis on Rayleigh-Taylor and Richtmyer-Meshkov mixing

A general buoyancy-drag model was recently proposed for describing all evolving stages of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities (Srebro et al 2003 Laser Part. Beams 21 347). We modify the model and then analyse the dynamical growth of RT and RM mixing zones using a spanwise homogeneous approximation, where two sides of the mixing zones are treated as distinct and homogeneously mixed fluids in the spanwise direction. The mixing zones are found to grow self-similarly when the ratio between the average amplitudes Zi(i ≤ 1: bubbles and i ≤ 2: spikes) of the mixing zones and the average wavelengths λicharacterizing perturbations remains constant, i.e., Zi/λi≤ b(A), where b(A) is a constant for a fixed Atwood number A. For a constant acceleration g, Zi≤ αiAgt2, and for an impulsive acceleration. With a simple form of b(A): and θideduced agree with recent LEM (linear electric motor) data over the experimental range of density ratio R. In addition, we find with Dα≤ 0.37 and with Dθ≤ 0.24. These agree well with recent experiments. Furthermore, as A → 1, α2→ 0.5 and θ2→ 1 are derived, consistent with recent theoretical predictions.