On Rayleigh-Taylor and Richtmyer-Meshkov Dynamics With Inverse-Quadratic Power-Law Acceleration - Hill, D. L.; Abarzhi, S. I. (Frontiers in Applied Mathematics and Statistics, 2022)
Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities are omnipresent in nature and technology at astrophysical and atomic scales, including stellar evolution, oceanic flows, plasma fusion, and scramjets. While RT and RM instabilities are sister phenomena, a link of RT-to-RM dynamics requires better understanding. This work focuses on the long-standing problem of RTI and RMI induced by accelerations varying as inverse-quadratic power-law with time for spatially extended three-dimensional flow periodic in the plane normal to the acceleration direction. We apply group theory to obtain solutions for the early-time linear and late-time nonlinear dynamics of RT/RM coherent structure of bubbles and spikes, and investigate the dependence of the solutions on the acceleration’s parameters and initial conditions. We find that the dynamics is of RT type for strong accelerations and is of RM type for weak accelerations, and identify the effects of the acceleration’s strength and the fluid density ratio on RT-to-RM transition. While for given problem parameters the early-time dynamics is uniquely defined, the solutions for the late-time dynamics form a continuous family parameterized by the interfacial shear and include special solutions for RT/RM bubbles/spikes. Our theory achieves good agreement with existing observations and elaborates benchmarks for future research and for better understanding of RT/RM relevant processes in nature and technology. Keywords: Rayleigh-Taylor instability, Richtmyer-Meshkov instability, coherent structures, interfacial dynamics, variable acceleration