On the evolution of flow topology in turbulent Rayleigh-Bénard convection
Authors: Dabbagh F. , Trias F. X. , Gorobets A. , Oliva A. 
Published: November 2016

Small-scale dynamics is the spirit of turbulence physics. It implicates many attributes of flow topology evolution, coherent structures, hairpin vorticity dynamics, and mechanism of the kinetic energy cascade. In this work, several dynamical aspects of the small-scale motions have been numerically studied in a framework of Rayleigh-Bénard convection (RBC). To do so, direct numerical simulations have been carried out at two Rayleigh numbers Ra = 108 and 1010, inside an air-filled rectangular cell of aspect ratio unity and π span-wise open-ended distance. As a main feature, the average rate of the invariants of the velocity gradient tensor (QG, RG) has displayed the so-called “teardrop” spiraling shape through the bulk region. Therein, the mean trajectories are swirling inwards revealing a periodic spin around the converging origin of a constant period that is found to be proportional to the plumes lifetime. This suggests that the thermal plumes participate in the coherent large-scale circulation and the turbulent wind created in the bulk. Particularly, it happens when the plumes elongate substantially to contribute to the large-scale eddies at the lower turbulent state. Supplementary small-scale properties, which are widely common in many turbulent flows have been observed in RBC. For example, the strong preferential alignment of vorticity with the intermediate eigenstrain vector, and the asymmetric alignment between vorticity and the vortex-stretching vector. It has been deduced that in a hard turbulent flow regime, local self-amplifications of straining regions aid in contracting the vorticity worms, and enhance the local interactions vorticity/strain to support the linear vortex-stretching contributions. On the other hand, the evolution of invariants pertained to the traceless part of velocity-times-temperature gradient tensor has also been considered in order to determine the role of thermals in the fine-scale dynamics. These new invariants show an incorporation of kinetic and thermal gradient dynamics that indicate directly the evolution and lifetime of thermal plume structures. By applying an identical approach, the rates of the new invariants have shown a symmetric cycling behaviour decaying towards two skew-symmetric converging origins at the lower Ra number. The trajectories near origins address the hot and cold coherent plumes that travel as an average large-scale heat flux in the sidewall vicinities, and denote a periodic spin period close to the plumes lifetime. At the hard turbulent case, the spiraling trajectories travel in shorter tracks to reveal the reduced lifetime of plumes under the dissipative and mixing effects. The turbulent background kinetic derivatives get self-amplified and the trajectories converge to a zero-valued origin indicating that there is no contribution from the plumes to the average coherent large scales of heat flux. These and other peculiar scrutinies on the small-scale motions in RBC have been enlightened, and may have a fruitful consequence on modelling approaches of buoyancy-driven turbulence.