Conditional statistics of thermal dissipation rate in turbulent Rayleigh-Bénard convection

Abstract

The statistical properties of the thermal dissipation rate in turbulent Rayleigh-Bénard convection in a cylindrical cell are studied by means of three-dimensional direct numerical simulations for a fixed Prandtl number Pr = 0.7 and aspect ratio Γ = 1. The Rayleigh numbers Ra are between 10(7) and 3 × 10(10). We apply a criterion that decomposes the cell volume into two disjoint subsets: the plume-dominated part and the turbulent background part. The plume-dominated set extends over the whole cell volume and is not confined to the boundary layers. It forms a complex spatial skeleton on which the heat is transported in the convection cell and its volume fraction decreases with increasing Rayleigh number. The latter finding holds also when the threshold, which separates both subvolumes, is varied. The Rayleigh number dependence of the mean moments and probability density functions of the thermal dissipation are analyzed on the subvolumes and related to other possible divisions of the convection volume, such as into boundary layer and bulk. The largest thermal dissipation events are always found in the plume-dominated subset.

Resolving the fine-scale structure in turbulent Rayleigh–Bénard convection

“…For example, the Nusselt number and the globally averaged thermal dissipation rates for both the whole cell and the bulk volume V b as shown in figure 7 agree quite well. We varied our Rayleigh number between 10 6 and 10 9 and compared with fits of the FDM data from [2,7,8], respectively. We did need to use a different prefactor for the bulk-averaged thermal dissipation rate since our subvolume V b was chosen differently.…”

“…The first two data sets are compared with fits to the FDM data (shown as dashed lines). For the whole cell V we take former results from [8], for the bulk volume V b we compare with data from [7]. In this case the prefactor is different since the subvolume V b was chosen differently.…”

Plume emission statistics in turbulent Rayleigh–Bénard convection

“…In addition, this choice of c matches the absolute value of the plume with the thermal boundary layer thickness, as will become apparent later on. A similar threshold based only on u z θ was used by Emran & Schumacher (2012), where they found no qualitative differences in their results when the threshold was varied by two orders of magnitude. Along the lines of what was already shown there, quantitatively our results do depend on the value of threshold c. In figure 3(d-f ) the results of applying this criterion to the temperature snapshots shown in figure 3(a-c) are depicted.…”

“…In addition, the dynamics of the LSC is highly non-trivial (Brown, Nikolaenko & Ahlers 2005;Ahlers et al 2009;Sugiyama et al 2010), affecting the collective motion of the thermal plumes through an opposing pressure gradient. This complicates the simple (two-dimensional) picture of a stationary LSC with thermal plumes moving alongside it that was sketched by Kadanoff (2001) (see figure 1), as Ching et al (2004) and Emran & Schumacher (2012) have shown that plumes are found in the centre of the cell and even throughout the entire volume. Recently, Ostilla-Mónico et al (2014) found in a Taylor-Couette (TC) flow that the boundary layer transition from laminar to turbulent occurs in plume-ejecting locations at lower driving than in the wind-sheared region.…”

Measurements of the dynamics of thermal plumes in turbulent mixed convection based on combined PIT and PIV

“…Moreover, the highest values of these quantities are found in regions where the sheet-like plumes collide, swirl up and form the stems of mushroom-like plumes, which develop into the bulk of the convection sample. Recently, Emran and Schuhmacher (2012) proposed a criterion based on both, temperature fluctuations and vertical velocity, in order to decompose the sample volume into a plumedominated part and the turbulent background part. They found that the plume-dominated part not only is limited to the thermal boundary layers, but instead extends over the whole sample volume.…”