Solutions to Buoyancy-Drag Equation for Dynamical Evolution of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Zone

With a self-similar parameter b(At) = Hi/λi, where At is the Atwood number, Hi and λi are the amplitude and wavelength of bubble (i = 1) and spike (i = 2) respectively, we derive analytically the solutions to the buoyancy-drag equation recently proposed for dynamical evolution of Rayleigh-Taylor and Richtmyer-Meshkov mixing zone. Numerical solutions are obtained with a simple form of b(At) = 1/(1 + At) and comparisons with recent LEM (linear electric motor) experiments are made, and an agreement is found with properly chosen initial conditions. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)