Logarithmic Mean Temperature Profiles and Their Connection to Plume Emissions in Turbulent Rayleigh-Bénard Convection

Abstract

Two-dimensional simulations of Rayleigh-Bénard convection at Ra = 5 × 10 10 show that vertical logarithmic mean temperature profiles can be observed in regions of the boundary layer where thermal plumes are emitted. The profile is logarithmic only in these regions and not in the rest of the boundary layer where it is sheared by the large scale wind and impacted by plumes. In addition, the logarithmic behavior is not visible in the horizontal average. The findings reveal that the temperature profiles are strongly connected to thermal plume emission and support a perception that parts of the boundary layer can be turbulent, while others are not. The transition to the ultimate regime, in which the boundary layers are considered to be fully turbulent, can therefore be understood as a gradual increases in fraction of the plume-emitting ('turbulent') regions of the boundary layer.

Boundary layer structure in turbulent Rayleigh–Bénard convection in a slim box

“…|A| = |A 1 |/ √ 4x(1 − x)). The relation between the log law of MTP and the emission of thermal plumes, previously suggested by a two-dimensional simula- tion of RBC [16], is confirmed in our 3D simulations, and the role of the adverse pressure gradient is emphasized.…”

“…The stress length of temperature * θ (z) is a three-layer function expressed as Eq. (16). Transition of the scaling of * θ from 3/2 to 5/2 occurs at z * sub .…”

“…The next transition of scaling from 5/2 to 1 is present at z * bu f . Jointly solving (15) and (16) yields an analytical function of the MTP as:…”

Phenomenology of buoyancy-driven turbulence: recent results

“…In a short review it is impossible to cover the vast number of results of buoyancy-driven turbulence. Here we could not describe recent results on the ultimate regime of turbulent convection [44,107], logarithmic profile of the boundary layer [96,108], new scaling of temperature [45], rotating convection [23], etc. Also we could not discuss SST for  Fr 1, which is very important for atmospheric turbulence.…”

“…There are intense research activities to test whether the ultimate regime exists or not. He et al [44] and others performed experiments on turbulent convection up to » Ra 10 15 and observed an increase in the Nusselt-number exponent β from 0.31 to 0.38, as well as logarithmic mean temperature profile [108]. Thus they claimed existence of the ultimate regime.…”