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

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 x 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 eta(t) similar to t(1/8), the kinetic-energy dissipation rate epsilon(u)(t) similar to t(-1/2), and the thermal dissipation rate epsilon(theta)(t) similar to 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)]. We further discuss the emergence of intermittency and anomalous scaling for high order moments of velocity and temperature differences. The scaling exponents xi(r)(p) of the pth-order temperature structure functions are shown to saturate to xi(r)(infinity) similar or equal to 0.78 +/- 0.15 for the highest orders, p similar to 10. The value of xi(r)(infinity) and the order at which saturation occurs are compatible with those of turbulent Rayleigh-Benard (RB) convection [A. Celani, T. Matsumoto, A. Mazzino, and M. Vergassola, " Scaling and universality in turbulent convection," Phys. Rev. Lett. 88, 054503 (2002)], supporting the scenario of universality of buoyancy-driven turbulence with respect to the different boundary conditions characterizing the RT and RB systems. (C) 2013 AIP Publishing LLC.