Effects of head loss on the growth of the Rayleigh–Taylor and the Richtmyer–Meshkov instabilities

Within the Zufiria’s potential flow theory generalized by Sohn (2007), we investigate the effects of head loss on the growth of the Rayleigh–Taylor and the Richtmyer–Meshkov instabilities. The nonlinear asymptotic solutions including the effects of head loss are obtained analytically for the bubble amplitude, velocity and curvature. We find that head loss depresses the bubble amplitude and velocity but enhances the bubble curvature. With an increase in the loss coefficient ζζ, the bubble amplitude and velocity decease rapidly, whereas the bubble curvature increases rapidly. A maximum of ζζ is found for the Rayleigh–Taylor instability, i.e., ζ→ζmax=0.5ζ→ζmax=0.5 which is independent of the Atwood number AA. But for the Richtmyer–Meshkov instability, ζmaxζmax depends on the Atwood number and ζmax=0.625-0.875ζmax=0.625-0.875 for A=0-1A=0-1. Our results of the bubble amplitude are found to be in good agreement with experimental data when we choose the suitable loss coefficients.