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 $2048\times 8193$ 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 $\eta (t)\sim t^{1/8}$, the kinetic-energy dissipation rate ${\epsilon }_u(t)\sim t^{-1/2}$, and the thermal dissipation rate ${\epsilon }_{\theta }(t)\sim t^{-1}$. All of these scaling properties are in excellent agreement with the theoretical predictions of the Chertkov model [Phys. Rev. Lett. \textbf{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 ${\xi }_p^r$ of the $p$th-order temperature structure functions are shown to saturate to ${\xi }_{\infty }^r\simeq 0.78\pm 0.15$ for the highest orders, $p\sim 10$. The value of ${\xi }_{\infty }^r$ and the order at which saturation occurs are compatible with those of turbulent Rayleigh-Bénard (RB) convection [Phys. Rev. Lett. \textbf{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.

17 pages, 17 figures, Accepted by Physics of Fluids

References in corpus (4)

• A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux
• Self-Similarity and Universality in Rayleigh-Taylor, Boussinesq Turbulence
• Horizontal Structures of Velocity and Temperature Boundary Layers in 2D Numerical Turbulent Rayleigh-Bénard Convection
• Comparative experimental study of local mixing of active and passive scalars in turbulent thermal convection

Cited by in corpus (3)

• Counter-gradient heat transport in two-dimensional turbulent Rayleigh-Bénard convection
• Toward analytic theory of the Rayleigh-Taylor instability: lessons from a toy model
• Effects of shock topology on temperature field in compressible turbulence