High-Reynolds number Rayleigh–Taylor turbulence

Abstract

The turbulence generated in the variable density Rayleigh–Taylor mixing layer is studied using the high-Reynolds number fully resolved 30723 numerical simulation of Cabot and Cook (Nature Phys. 2 (2006), pp. 562–568). The simulation achieves bulk Reynolds number, Re = H Ḣ/ν = 32,000, turbulent Reynolds number, Re t = [ktilde] 2/νϵ = 4600, and Taylor Reynolds number, R λ = 170. The Atwood number, A, is 0.5, and the Schmidt number, Sc, is 1. Typical density fluctuations, while modest, being one quarter the mean density, lead to non-Boussinesq effects. A comprehensive study of the variable density energy budgets for the kinetic energy, mass flux and density specific volume covariance equations is undertaken. Various asymmetries in the mixing layer, not seen in the Boussinesq case, are identified and explained. Hypotheses for the variable density turbulent transport necessary to close the second moment equations are studied. It is found that, even though the layer width becomes temporally self-similar relatively fast, the transient effects in the energy spectrum remain important for the duration of the simulation. Thus, the dissipation does not track the spectral energy cascade rate and the integral lengthscale does not follow the expected Kolmogorov scaling, [ktilde] 3/2/ϵ. As a result, the popular eddy diffusivity expression, ν t ∼[ktilde] 2/ϵ, does not model the temporal variation of the turbulent transport in any of the moment equations. An eddy diffusivity based on a lengthscale related to the layer width is found to work well in a gradient transport hypothesis for the turbulent transport; however, that lengthscale is a global quantity and does not lead to pointwise, local closure. Therefore, although the transient effects may vanish asymptotically, it is suggested that, even long after the onset of the self-similar growth, two separate lengthscale equations (or equivalent) are needed in a moment closure strategy for Rayleigh–Taylor turbulence: one for the turbulent transport and the other for the dissipation. Despite the fact that the intermediate scales are nearly isotropic, the small scales have a persistent anisotropy; this is due to a cancellation between the viscous and nonlinear effects, so that the anisotropic buoyancy production remains important at the smallest scales.