Viscous boundary layer properties in turbulent thermal convection in a cylindrical cell: the effect of cell tilting

Abstract

We report an experimental study of the properties of the velocity boundary layer in turbulent Rayleigh-Bénard convection in a cylindrical cell. The measurements were made at Rayleigh numbers $Ra$ in the range $2.8\times 10^8<Ra<5.6\times 10^9$ and were conducted with the convection cell tilted with an angle $\theta$ relative to gravity, at $\theta =0.5^o$, $1.0^o$, $2.0^o$, and $3.4^o$, respectively. The fluid was water with Prandtl number $Pr=5.3$. It is found that at small tilt angles ($\theta \le 1^o$), the measured viscous boundary layer thickness ${\delta }_v$ scales with the Reynolds number $Re$ with an exponent close to that for a Prandtl-Blasius laminar boundary layer, i.e. ${\delta }_v\sim R{e}^{-0.46\pm 0.03}$. For larger tilt angles, the scaling exponent of ${\delta }_v$ with $Re$ decreases with $\theta$. The normalized mean horizontal velocity profiles measured at the same tilt angle but with different $Ra$ are found to have an invariant shape. But for different tilt angles, the shape of the normalized profiles is different. It is also found that the Reynolds number $Re$ based on the maximum mean horizontal velocity scales with $Ra$ as $Re\sim R{a}^{0.43}$ and the Reynolds number $R{e}_{\sigma }$ based on the maximum rms velocity scales with $Ra$ as $R{e}_{\sigma }\sim R{a}^{0.55}$, with both exponents do not seem to depend on the tilt angle $\theta$. We also examined the dynamical scaling method proposed bys Zhou and Xia [Phys. Rev. Lett. 104, 104301 (2010)] and found that in both the laboratory and the dynamical frames the mean velocity profiles show deviations from the theoretical Prandtl-Blasius profile, with the deviations increase with $Ra$. But profiles obtained from dynamical scaling in general have better agreement with the theoretical profile. It is also found that the effectiveness of this method appears to be independent of $Ra$.

28 pages,23 figures

References in corpus (3)

• Boundary layer structure in turbulent Rayleigh-Benard convection
• Thermal boundary layer profiles in turbulent Rayleigh-Bénard convection in a cylindrical sample
• Horizontal Structures of Velocity and Temperature Boundary Layers in 2D Numerical Turbulent Rayleigh-Bénard Convection

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