A study of bubble growth in the compressible Rayleigh–Taylor and Richtmyer–Meshkov instabilities

摘要

Within the framework of modified Layzer-type potential flow theory [V. N. Goncharov, “Analytical model of nonlinear, single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers,” Phys. Rev. Lett. 88 , 134502 (2002)], we study bubble growth in compressible Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities. It is known from adiabatic equations that the density ρ and adiabatic index γ are compressibility-related factors for a given static pressure p . Here, we introduce a dynamically varying stagnation point pressure P ? = p ± 1 2 ρ ? η ? 0 2 , which relates time-varying quantities, such as fluid density ρ ? , pressure P ? , and bubble tip velocity η ? 0 , and then, we analytically derive the governing equations for time evolution of bubbles in the RT and RM instabilities of compressible fluids. For the RT instability, the upper fluid adiabatic index γ u and density ρ u increase the bubble amplitude and velocity, but they decrease the bubble curvature radius at the early stage, while the lower fluid adiabatic index γ l and density ρ l have opposite effects on those of γ u and ρ u , which is consistent with recent results. For the RM instability, γ u and ρ u decrease the bubble amplitude and velocity, but they increase the bubble curvature radius at the early stage; however, γ l and ρ l have opposite effects on those of γ u and ρ u . Moreover, we find a good agreement between our three-dimensional results of the RM bubble amplitude and recent numerical simulations.