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Multi-fluid mixing in a system with three stratified layers is explored using two-dimensional compressible direct numerical simulations (DNS) by solving fully compressible multi-species Navier-Stokes equations. All configuration cases under investigation consist of at least one acceleration-driven Rayleigh-Taylor unstable interface where the direction of the acceleration is from the heavier to the lighter fluids to initiate the chaotic mixing. The DNS are initialized with isopycnic background stratification, where the species densities of the three fluids are initially constant over the domain, and also they are benefited from the adaptive mesh refinement (AMR) to reduce the computational cost. We investigate four cases with the global Atwood number of 0.04 where the stratified layers along the acceleration direction (from bottom to top) have heavy-intermediate-light, heavy-light-light, heavy-light-intermediate, and heavy-light-heavy densities, and each case is studied with two different distances between the first and third fluid layers. It is found that the globally unstable case with heavy-intermediate-light densities, which has two unstable interfaces, exhibits symmetric mixing during the flow evolution and eventually behaves similarly to the classical two-layer Rayleigh-Taylor instability (RTI) flows. This finding is consistent with the observation in previous three-layer RTI experiments. The case with heavy-light-light densities is performed for comparison purposes, and it practically only has a single-stratified interface similar to the two-layer RTI problem. For the remaining two cases, the top interface of the three-layer RTI is stably stratified. It is shown that for the cases where the top interface is neutrally stratified (e.g., heavy-light-light case) or weakly stratified (e.g., heavy-light-intermediate case), upward pure fluids penetration is larger compared to the heavy-light-heavy case, whose top interface is initially strongly stable. In addition to the study on large-scale RTI entrainment, we also present mixedness and vortical dynamics of the flows. 

Rayleigh–Taylor instability, RTI, occurs at the interface separating two fluids subjected to acceleration when the density gradient and the acceleration are in opposite directions. Previous scientific research primarily considered RTI under the incompressible assumption, which may not be valid in many high-energy-density engineering applications and astrophysical phenomena. In this study, the compressibility effects of the background isothermal stratification strength on multi-mode two-dimensional RTI are explored using fully compressible multi-species direct numerical simulations. Cases under three different isothermal Mach numbers – Ma=0.15,  0.3,  and  0.45 – are investigated to explore weakly, moderately, and strongly stratified compressible RTI, respectively, at an Atwood number of 0.04. Unlike incompressible RTI, an increase in the flow compressibility through the strength of the background stratification can suppress the RTI growth and can lead to a termination of the RTI mixing layer growth with a highly molecularly mixed state. Our findings suggest that even at the chosen relatively low Atwood number, the variable-density effects can be significantly enhanced due to an increase in the background stratification for the compressible RTI as different spatial profiles become noticeably asymmetric across the mixing layer for the strongly stratified case. In addition, this study compares the chaotic behavior of the cases by studying the transport of the turbulent kinetic energy as well as the vortex dynamics. The Reynolds number dependence of the results is also examined with three different Reynolds numbers, and the findings for the large-scale mixing and flow quantities of interest are shown to be universal in the range of the Reynolds numbers studied.