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 e(t) t 1/8, the kinetic energy dissipation rate e u (t) t 1/2, and the thermal dissipation rate eth(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 (Year: 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 of the pth order temperature structure functions are shown to saturate to for the highest orders, p 10. The value of 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 (Year: 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. x p r x r 0.78 0.15 x r