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 Z(i) (i = 1: bubbles and i = 2: spikes) of the mixing zones and the average wavelengths lambda(i) characterizing perturbations remains constant, i.e., Z(i)/lambda(i) = b(A), where b(A) is a constant for a fixed Atwood number A. For a constant acceleration g, Z(i) = alpha(i)Agt(2), and Z(i) proportional to ti(theta i) for an impulsive acceleration. With a simple form of b(A): b(A) = 1/1+A, alpha(i) and theta i deduced agree with recent LEM (linear electric motor) data over the experimental range of density ratio R. In addition, we find alpha(2) similar to alpha(1)R(D alpha) with D-alpha = 0.37 and theta(2) similar to theta(1) R-D theta with D-theta = 0.24. These agree well with recent experiments. Furthermore, as A -> 1, alpha(2) -> 0.5 and theta(2) -> 1 are derived, consistent with recent theoretical predictions.