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Logarithmic variance profiles and the corresponding {\lowercase {$ f^{-1}$}} spectra of temperature fluctuations in turbulent Rayleigh-B\'enard convection
Xiaozhou He, Dennis van Gils, Eberhard Bodenschatz, Guenter Ahlers
Session: Thermally driven turbulence 1
Session starts: Thursday 27 August, 10:30
Presentation starts: 10:45
Room: Room I

Xiaozhou He (Max Planck Institute for Dynamics and Self-Organization)
Dennis van Gils (Max Planck Institute for Dynamics and Self-Organization)
Eberhard Bodenschatz (Max Planck Institute for Dynamics and Self-Organization)
Guenter Ahlers (Department of Physics, University of California, Santa Barbara, CA, USA)

We report experimental results for the temperature variance $\sigma^2(z)$ and the corresponding frequency spectra $P(f)$ in turbulent Rayleigh-B\'enard convection (RBC) in a cylindrical sample of aspect ratio $\Gamma \equiv D/L = 1.00$ ($D = 1.12$ m is the diameter and $L = 1.12$ m the height). The measurements were conducted in the Rayleigh-number range $10^{11} \alt$ Ra $\alt 1.35\times10^{14}$ and Pr $\simeq 0.8$. For Ra $= 1.35\times 10^{14}$, $\sigma^2(z)$ could be described well by a logarithmic dependence on the vertical position $z$ in a range of $z^*_1 \alt z \alt z^*_2$ with $z^*_1 \simeq 70 \lambda_{\theta}$ and $z^*_2 = 0.1L$. Here $\lambda_\theta \equiv L/(2Nu)$ is the thickness of a thin thermal sublayer adjacent to the horizontal plate where the heat flux (denoted by the Nusselt number $Nu$) is carried mostly by thermal diffusion. In the log layer, we found that the temperature spectra had a significant frequency range over which $P(f) \sim f^{-\alpha}$ with $\alpha$ close to $1$. As Ra decreased, $\lambda_\theta$ increased so that the log layer became thinner. At Ra $= 2.05 \times 10^{11}$, $z^*_2 \alt z^*_1$ and therefore there was no range for a log layer. Correspondingly, the temperature spectrum near the horizontal plate did not have the $f^{-1}$ scaling form either.