Horizontal Structures of Velocity and Temperature Boundary Layers in 2D Numerical Turbulent Rayleigh-B\'{e}nard Convection

TL;DR

This study analyzes the boundary layer structures in 2D turbulent Rayleigh-Bénard convection, demonstrating that dynamical frame methods reveal Prandtl-Blasius laminar profiles in velocity and temperature fields.

Contribution

It shows that dynamical frame scaling aligns instantaneous boundary layer profiles with classical laminar solutions, providing a more accurate characterization of boundary layers in turbulent convection.

Findings

Instantaneous profiles match Prandtl-Blasius laminar profiles.

Dynamical reference frames yield consistent boundary layer thicknesses.

Traditional time-averaged profiles can produce unphysical boundary layer measurements.

Abstract

We investigate the structures of the near-plate velocity and temperature profiles at different horizontal positions along the conducting bottom (and top) plate of a Rayleigh-B\'{e}nard convection cell, using two-dimensional (2D) numerical data obtained at the Rayleigh number Ra=10^8 and the Prandtl number Pr=4.4 of an Oberbeck-Boussinesq flow with constant material parameters. The results show that most of the time, and for both velocity and temperature, the instantaneous profiles scaled by the dynamical frame method [Q. Zhou and K.-Q. Xia, Phys. Rev. Lett. 104, 104301 (2010) agree well with the classical Prandtl-Blasius laminar boundary layer (BL) profiles. Therefore, when averaging in the dynamical reference frames, which fluctuate with the respective instantaneous kinematic and thermal BL thicknesses, the obtained mean velocity and temperature profiles are also of Prandtl-Blasius type for nearly all horizontal positions. We further show that in certain situations the traditional definitions based on the time-averaged profiles can lead to unphysical BL thicknesses, while the dynamical method also in such cases can provide a well-defined BL thickness for both the kinematic and the thermal BLs.