Local dissipation scales in two-dimensional Rayleigh-Taylor turbulence

Abstract

We examine the distribution of the local dissipation scale η, Q(η), and its temporal evolution in two-dimensional (2D) Rayleigh-Taylor (RT) turbulence using direct numerical simulations at small Atwood number and unit Prandtl number. Within the self-similarity regime of the mixing zone evolution, distributions of η at small scales are found to be insensitive to the large-scale anisotropy of the system and independent of position and of the temporal evolution of the mixing zone. Our results further reveal that the present measured Q(η) agrees with those previously observed in homogeneous isotropic turbulence and in turbulent pipe flows, at least for the smallest scales around the classical Kolmogorov dissipation scale. However, the RT case seems to show a different trend from the other two cases for large scales, which may attributed to the absence of the inertial-range intermittency for the velocity field in 2D RT turbulence.

Incompressible Rayleigh–Taylor Turbulence

“…From these two remarks it immediately follows that temperature fluctuations around T (z) are homogeneous and the same is for the velocity: this is indeed forced by temperature fluctuations, the horizontally averaged temperature being balanced by the averaged pressure field as stated above. The above scenario is confirmed by a deep analysis on the distribution of the local dissipation scale carried out in two-dimensions by Qiu et al (2014). The tendency toward isotropy restoration of small-scale fluctuations has been numerically verified by Biferale et al (2010) in two dimensions and by Bo↵etta et al (2009) and Bo↵etta et al (2010d) in three dimensions, and by Ramaprabhu & Andrews (2004) in an experimental investigation.…”

Statistics of velocity and temperature fluctuations in two-dimensional Rayleigh-Bénard convection

“…The numerical method is based on a compact fourth-order finite-difference scheme introduced by Liu et al [37], and it has been explained by Zhou [38] and Huang and Zhou [39]. Recently, we have employed the same numerical code to investigate the small-scale cascade properties in the 2D Rayleigh-Taylor system [40][41][42]. The grid spacing is uniform in both horizontal and vertical directions, and the number of grid points is increased from 129×129 to 2049×2049 as Ra increases from 10 6 to 10 10 in the present work.…”

Kinetic energy and enstrophy transfer in compressible Rayleigh–Taylor turbulence

“…, where the perturbation wavenumbers and in the and directions are set in a range of (or ) with the amplitude and random phases and (Clark 2003; Boffetta et al. 2009; Qiu, Liu & Zhou 2014).…”