Self-similarity and universality in Rayleigh–Taylor, Boussinesq turbulence

Abstract

We report and discuss case study simulations of the Rayleigh-Taylor instability in the Boussinesq, incompressible regime developed to turbulence. Our main focus is on a statistical analysis of density and velocity fluctuations inside of the already developed and growing in size mixing zone. Novel observations reported in the article concern self-similarity of the velocity and density fluctuations spectra inside of the mixing zone snapshot, independence of the spectra of the horizontal slice level, and universality showing itself in a virtual independence of the internal structure of the mixing zone, measured in the re-scaled spatial units, of the initial interface perturbations.

Temporal evolution and scaling of mixing in two-dimensional Rayleigh-Taylor turbulence

“…(5)]. For the 3D case, this was indeed observed by previous numerical studies 19,21 . In this study, we adopt the idea of Vladimirova & Chertkov 19 to investigate the relation between L(t) and h(t) in 2D RT flow.…”

“…For velocity, a best linear fit yields L u /h ≃ 0.12 and L w /h ≃ 0.16 for the integral scales based on the horizontal and vertical components of the velocity, respectively. These values are much larger than those of L u /h ≃ 0.024 and L w /h ≃ 0.059 obtained in 3D case 19,21 , suggesting that the 2D large-scale vortices in the mixing zone grow much faster than their 3D counterparts. In addition, the relative difference between L u /h and L w /h of the present case is smaller than that of the 3D case, suggesting again a relatively lower degree of anisotropy possessed by 2D RT flow.…”

“…Using dimensional analysis and self-similar assumptions 10,19,27 , one expects that the growth of h(t) follows the accelerated law, i.e.…”

“…Although RT turbulence is of great importance and has been studied for many decades, there are still some open issues 10,11 . Specifically, for the past decade, many studies [12][13][14][15][16][17][18][19][20][21][22][23][24][25] have focused on small-scale turbulent fluctuations in both two-(2D) and three-dimensional (3D) RT turbulence. In two dimensions, Chertkov 15 proposed a phenomenological theory.…”

On the Kolmogorov inertial subrange developing from Richtmyer-Meshkov instability

“…Later, this phenomenological theory was supported by numerical simulations. [7][8][9] The theoretical work of Chertkov 6 together with its numerical validation by Boffetta et al 9 led to a coherent and consistent picture of Rayleigh-Taylor turbulence as a Kolmogorov cascade of kinetic energy driven by unstable stratification.…”