REYNOLDS DECOMPOSITION OF TURBULENCE CONTAINING SUPER-COHERENT STATES

Abstract

We address the problem that occurs when time average values of mean and higher-order statistics of certain flows fail to exhibit the symmetry properties imposed by boundary conditions and physics. Such failures render determinations of the mean fields suspect, making it difficult, or even incorrect to apply Reynolds decomposition. We have been studying turbulent Rayleigh-Benard convection (RBC) in a 6.3:1 (diameter:depth) aspect-ratio vertical cylinder (Sakievich, et al. 2016), and it will be used as example to illustrate and explain this phenomenon. However, there are reasons to believe that the concepts that are developed from RBC pertain to other turbulent flows. In unit aspect ratio cylinders, it is commonly observed that the mean flow is non-zero (Bodenschatz, et al.; Emran, et al. 2015). We find from HPC simulations that turbulent RBC in a wide circular cylinder characteristically contains large-scale motions that are mean-square-periodic in the azimuthal-direction. In plan view they look like a somewhat randomly centered hub of rising (falling) fluid from which ‘spokes’ emanate in radial directions, iFgure 1. The spokes are convergence zones of warm (cool) fluid rising (falling) between horizontal, radially oriented, counter-rotating roll-cells. The most energetic roll cells have azimuthal periodicity Figure 1. RBC flow pattern at 109 Rayleigh number in a cylindrical geometry The flow is averaged over 600 free-fall times.