Compressible Rayleigh–Taylor turbulent mixing layer between Newtonian miscible fluids

Abstract

Rayleigh–Taylor instability induced turbulence between two compressible miscible Newtonian fluids is studied in a strongly stratified configuration at a moderate Atwood number. A direct numerical simulation has been carried out with an auto-adaptive multidomain Chebyshev–Fourier–Fourier numerical method. The spatial resolution is increased up to $(9\times 100)\times 1000^{2}=900M$ collocation points. These numerical data are compared with those obtained from a simulation carried out at a lower Reynolds number and at the same Atwood number, and those obtained from a simulation carried out within the Boussinesq approximation at the same Reynolds number. A comprehensive data analysis is reported. Physical-variable mean profiles – density, concentration, temperature, entropy, velocity, vorticity, helicity and palinstrophy – are provided. Anisotropy is studied in the spectral space. The intermediate-scale isotropy and the small-scale anisotropy are exhibited for the scalars, i.e. concentration and temperature. Velocity is anisotropic at all scales but this anisotropy is more marked at small scales. The data are also analysed with the Favre-averaged equations. Sources of the turbulent kinetic energy, mass flux, root-mean-square density and energy equations are analysed. Compressibility effects are discussed in particular with the Kovàsznay-mode decomposition. A statistical study is reported where skewnesses, flatnesses and probability density functions (PDFs) are displayed and commented. A flow visualization is also given. Finally, the temperature field appears to be the slave of the mixing. This conclusion is drawn from the comparison of power spectra, anisotropy spectra, skewnesses, flatnesses, PDFs and correlation coefficients. There is however a significant time lag between the density and temperature evolution.