Turbulent Boundary Layer in High Rayleigh Number Convection in Air

Flow visualizations and particle image velocimetry measurements in the boundary layer of a Rayleigh-Bénard experiment are presented for the Rayleigh number $\mathrm{Ra}=1.4\times {10}^{10}$. Our visualizations indicate that the appearance of the flow structures is similar to ordinary (isothermal) turbulent boundary layers. Our particle image velocimetry measurements show that vorticity with both positive and negative sign is generated and that the smallest flow structures are 1 order of magnitude smaller than the boundary layer thickness. Additional local measurements using laser Doppler velocimetry yield turbulence intensities up to $I=0.4$ as in turbulent atmospheric boundary layers. From our observations, we conclude that the convective boundary layer becomes turbulent locally and temporarily although its Reynolds number $\mathrm{Re}\approx 200$ is considerably smaller than the value 420 underlying existing phenomenological theories. We think that, in turbulent Rayleigh-Bénard convection, the transition of the boundary layer towards turbulence depends on subtle details of the flow field and is therefore not universal.

Figure 1

Experimental setup for the flow visualization in a Rayleigh-Bénard cell of rectangular shape.

Figure 2

Snapshots of contrasting flow states above the center of the heating plate (position 1) separated by only a few seconds. The upper pictures (a),(c) show streaks of droplets of about $1\mu \mathrm{m}$ size added to the flow, the lower plots (b),(d) show the corresponding vector field, and the color shows the local vorticity.

Figure 3

Flow field at position 2 (a),(b) and position 3 (c),(d) close to the left and the right sidewall, respectively. The upper pictures show streaks of small droplets of about $1\mu \mathrm{m}$ size added to the flow, the lower plots show the corresponding vector field as well as the local vorticity.

Figure 4

Profile of the turbulence intensity $I(z^{+})$. The dashed line indicates the boundary layer thickness ${\delta }_{99}^{+}={\delta }_{99}{u}_{\tau }/\nu$.