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

TL;DR

This study uses high-resolution simulations to analyze the temporal evolution and scaling laws of 2D Rayleigh-Taylor turbulence, confirming theoretical models and revealing universal features of buoyancy-driven turbulence.

Contribution

First detailed numerical validation of Bolgiano-Obukhov scaling and universality in 2D Rayleigh-Taylor turbulence at high resolution.

Findings

Buoyancy balances inertial forces at all scales below the integral length.

Scaling laws match Chertkov model predictions.

Evidence of intermittency and anomalous scaling in 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 $2048\times8193$ 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 $\varepsilon_u(t)\sim t^{-1/2}$, and the thermal dissipation rate $\varepsilon_{\theta}(t)\sim t^{-1}$. 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 $\xi^r_p$ of the $p$th-order temperature structure functions are shown to saturate to $\xi^r_{\infty}\simeq0.78\pm0.15$ for the highest orders, $p\sim10$. The value of $\xi^r_{\infty}$ and the order at which saturation occurs are compatible with those of turbulent Rayleigh-B\'{e}nard (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.