Bubble dynamics of Rayleigh-Taylor flow

A flow of semi-bounded Rayleigh-Taylor instability (SB-RTI) is constructed and simulated to understand the bubble dynamics of the multi-mode Rayleigh-Taylor mixing (MM-RTM). SB-RTI is similar to the well-known single-mode Rayleigh-Taylor instability (SM-RTI), and it acts as a bridge from SM-RTI to MM-RTM. This idea is inspired by Meshkov's recent experimental observation on the structure of the mixing zone of MM-RTM [E. E. Meshkov, J. Exp. Theor. Phys. 126, 126-131 (2018)]. We suppose that the bubble mixing zone consists of two parts, namely, the turbulent mixing zone at the center and the laminar-like mixing zone nearby the edge. For the latter, the bubble fronts are situated in an environment similar to that of SM-RTI bubbles in the potential flow stage, but with a much looser environment between neighboring bubbles. Therefore, a semi-bounded initial perturbation is designed to produce a bubble environment similar to that in MM-RTM. A non-dimensional potential speed of FrpSB approximate to 0.63 is obtained in SB-RTI, which is larger than that of FrpSM=0.56 in SM-RTI. Combining this knowledge and the widely reported quadratic growth coefficient of alpha (b) approximate to 0.025 in the short-wavelength MM-RTM, we derive beta equivalent to D(t)/h(b)(t) approximate to (1 + A)/4. This relation is consistent with the MM-RTM simulations from Dimonte et al. [Phys. Fluids 16, 1668-1693 (2004)]. The current three-dimensional and previous two-dimensional results [Zhou et al., Phys. Rev. E 97, 033108 (2018)] support a united mechanism of bubble dynamics in short-wavelength MM-RTM.