Investigating Rayleigh–Taylor instabilities using a statistically stationary and homogeneous simulation framework

Homogeneous buoyant turbulence (HBT) is developed as a novel direct numerical simulation (DNS) framework for modelling the small scales of turbulence in a temporally evolving Rayleigh–Taylor instability (TRT). Using a set of coordinate and variable transformations, statistical stationarity and homogeneity in all three directions are introduced to the TRT flow variables. These transformations produce a set of source terms in the governing equations, which, within a region surrounding the TRT midplane, reduce to just two non-negligible terms in the momentum and scalar transport equations. When applied to a periodic box domain, the new governing equations are verified to produce a stationary, homogeneous flow. Validation is performed for HBT against a large-scale TRT DNS, where probability density functions, the anisotropy of the kinetic energy and the anisotropy of the velocity gradient tensor are successfully reproduced. Turbulence spectra of HBT also show strong fidelity to the TRT spectra at the midplane, including the velocity and density spectra and the density–vertical velocity cospectrum. Significant computational savings are afforded by HBT compared to TRT DNS, owing to its smaller domain and shorter transient period. Furthermore, HBT’s statistical stationarity and homogeneity facilitates the estimation of turbulence statistics to a high degree of precision. The framework has potential applications in the development of subgrid scale models for buoyant flows.