Comparison of two- and three-dimensional simulations of miscible Rayleigh-Taylor instability

A comparison of two-dimensional and three-dimensional high-resolution numerical large-eddy simulations of planar, miscible Rayleigh-Taylor instability flows is presented. The resolution of the three-dimensional simulation is sufficient to attain a fully turbulent state. A number of different statistics from the mixing region (e.g., growth rates, probability distribution functions, mixedness measures, and spectra) are used to demonstrate that two-dimensional flow simulations differ substantially from the three-dimensional one. It is found that the two-dimensional flow grows more quickly than its three-dimensional counterpart at late times, develops larger structures, and is much less well mixed. These findings are consistent with the concept of inverse cascade in two-dimensional flow, as well as the influence of a reduced effective Atwood number on miscible flow.