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

Abstract

We report a high-resolution numerical study of two-dimensional (2D) miscible Rayleigh-Taylor (RT) incompressible turbulence with the Boussinesq approximation. An ensemble of 100 independent realizations were performed at small Atwood number and unit Prandtl number with a spatial resolution of 2048 × 8193 grid points. Our main focus is on the temporal evolution and the scaling behavior of global quantities and of small-scale turbulence properties. Our results show that the buoyancy force balances the inertial force at all scales below the integral length scale and thus validate the basic force-balance assumption of the Bolgiano-Obukhov scenario in 2D RT turbulence. It is further found that the Kolmogorov dissipation scale η(t) ∼ t1/8, the kinetic-energy dissipation rate ɛu(t) ∼ t−1/2, and the thermal dissipation rate ɛθ(t) ∼ t−1. All of these scaling properties are in excellent agreement with the theoretical predictions of the Chertkov model [“Phenomenology of Rayleigh-Taylor turbulence,” Phys. Rev. Lett. 91, 115001 (2003)]10.1103/PhysRevLett.91.115001. We further discuss the emergence of intermittency and anomalous scaling for high order moments of velocity and temperature differences. The scaling exponents \documentclass[12pt]{minimal}\begin{document}$\xi ^r_p$\end{document}ξpr of the pth-order temperature structure functions are shown to saturate to \documentclass[12pt]{minimal}\begin{document}$\xi ^r_{\infty }\simeq 0.78 \pm 0.15$\end{document}ξ∞r≃0.78±0.15 for the highest orders, p ∼ 10. The value of \documentclass[12pt]{minimal}\begin{document}$\xi ^r_{\infty }$\end{document}ξ∞r and the order at which saturation occurs are compatible with those of turbulent Rayleigh-Bénard (RB) convection [A. Celani, T. Matsumoto, A. Mazzino, and M. Vergassola, “Scaling and universality in turbulent convection,” Phys. Rev. Lett. 88, 054503 (2002)]10.1103/PhysRevLett.88.054503, supporting the scenario of universality of buoyancy-driven turbulence with respect to the different boundary conditions characterizing the RT and RB systems.