Self-similarity of a Rayleigh-Taylor mixing layer at low Atwood number with a multimode initial perturbation

High-fidelity large eddy simulation (LES) of a low-Atwood number ($A$ = 0.05) Rayleigh-Taylor mixing layer is performed using the tenth-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or \emph{generation}. The database is then analyzed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that the present database reaches a high degree of self-similarity after approximately 4.5 generations. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the $k$-$L$-$a$ and BHR-2 Reynolds-averaged Navier-Stokes (RANS) models. The $k$-$L$-$a$ model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results.