Thermal boundary layer profiles in turbulent Rayleigh-B\'enard convection in a cylindrical sample

TL;DR

This study numerically examines the near-plate temperature profiles in turbulent Rayleigh-Bénard convection within a cylindrical sample, revealing closer alignment with laminar boundary layer profiles when using a dynamical reference frame, especially at higher Rayleigh numbers and lower Prandtl numbers.

Contribution

First application of the dynamical frame method to 3D turbulent Rayleigh-Bénard convection, showing improved agreement with laminar boundary layer profiles compared to fixed reference frames.

Findings

Profiles in the dynamical frame are closer to laminar profiles.

Deviation increases with decreasing Prandtl number.

Deviation increases with increasing Rayleigh number.

Abstract

We numerically investigate the structures of the near-plate temperature profiles close to the bottom and top plates of turbulent Rayleigh-B\'{e}nard flow in a cylindrical sample at Rayleigh numbers Ra=10^8 to Ra=2\times10^{12} and Prandtl numbers Pr=6.4 and Pr=0.7 with the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010)] thus extending previous results for quasi-2-dimensional systems to 3D systems for the first time. The dynamical frame method shows that the measured temperature profiles in the spatially and temporally local frame are much closer to the temperature profile of a laminar, zero-pressure gradient boundary layer according to Pohlhausen than in the fixed reference frame. The deviation between the measured profiles in the dynamical reference frame and the laminar profiles increases with decreasing Pr, where the thermal BL is more exposed to the bulk fluctuations due to the thinner kinetic BL, and increasing Ra, where more plumes are passing the measurement location.