Three-dimensional multimode Rayleigh–Taylor and Richtmyer–Meshkov instabilities at all density ratios

Abstract

The three-dimensional~3D! turbulent mixing zone~TMZ! evolution under Rayleigh-Taylor and Richtmyer-Meshkov conditions was studied using two approaches. First, an extensive numerical study was made, investigating the growth of a random 3D perturbation in a wide range of density ratios. Following that, a new 3D statistical model was developed, similar to the previously developed two-dimensional~2D! statistical model, assuming binary interactions between bubbles that are growing at a 3D asymptotic velocity. Confirmation of the theoretical model was gained by detailed comparison of the bubble size distribution to the numerical simulations, enabled by a new analysis scheme that was applied to the 3D simulations. In addition, the results for the growth rate of the 3D bubble front obtained from the theoretical model show very good agreement with both the experimental and the 3D simulation results. A simple 3D drag-buoyancy model is also presented and compared with the results of the simulations and the experiments with good agreement. Its extension to the spike-front evolution, made by assuming the spikes' motion is governed by the singlemode evolution determined by the dominant bubbles, is in good agreement with the experiments and the 3D simulations. The good agreement between the 3D theoretical models, the 3D numerical simulations, and the experimental results, together with the clear differences between the 2D and the 3D results, suggest that the discrepancies between the experiments and the previously developed models are due to geometrical effects.

Analysis of Rayleigh-Taylor Instability: Statistics on Rising Bubbles and Falling Spikes

“…We note that in the paper by Kartoon et al [5], they observe a ratio of 0.5 for rising bubbles vs. all bubbles using their definition of a rising bubble.…”

“…In related work, Kartoon et al [5] define a rising bubble in the Rayleigh-Taylor instability as one which is accelerating, while a decelerating bubble is considered to be sinking. However, for their analysis of the Richtmyer-Meshkov instability, they use a velocity-based criterion as in the work of Gardner et al [3].…”

“…We also calculate the height of the rising bubbles, and correspondingly, the depth of the falling spikes, using the definition proposed by Kartoon et al in [5]. They consider the bubble front height to be the average over the tips of the rising bubbles.…”

“…As in the paper by Kartoon at al. [5], we also include the ratio of the rising bubbles (falling spikes) to all bubbles (spikes). We observe the following regarding these ratios.…”

Understanding the Structure of the Turbulent Mixing Layer in Hydrodynamic Instabilities

“…al. [9] segment bubbles from a set of small simulations using a vertical velocity criterion. Their method is not fully described in their paper, making it difficult to assess its robustness.…”