Logarithmic spatial variations and universal f-1 power spectra of temperature fluctuations in turbulent Rayleigh-Bénard convection.
We report measurements of the temperature variance σ(2)(z,r) and frequency power spectrum P(f,z,r) (z is the distance from the sample bottom and r the radial coordinate) in turbulent Rayleigh-Bénard convection (RBC) for Rayleigh numbers Ra = 1.6 × 10(13) and 1.1 × 10(15) and for a Prandtl number Pr ≃ 0.8 for a sample with a height L = 224 cm and aspect ratio D/L=0.50 (D is the diameter). For z/L ≲ 0.1 σ(2)(z,r) was consistent with a logarithmic dependence on z, and there was a universal (independent of Ra, r, and z) normalized spectrum which, for 0.02 ≲ fτ(0) ≲ 0.2, had the form P(fτ(0)) = P(0)(fτ(0))(-1) with P(0) = 0.208 ± 0.008 a universal constant. Here τ(0) = sqrt[2R] where R is the radius of curvature of the temperature autocorrelation function C(τ) at τ = 0. For z/L ≃ 0.5 the measurements yielded P(fτ(0))∼(fτ(0))(-α) with α in the range from 3/2 to 5/3. All the results are similar to those for velocity fluctuations in shear flows at sufficiently large Reynolds numbers, suggesting the possibility of an analogy between the flows that is yet to be determined in detail.
Max Planck Institute for Dynamics and Self Organization, D-37073 Göttingen, Germany.
Xiaozhou
X
He
Max Planck Institute for Dynamics and Self Organization, D-37073 Göttingen, Germany.
Dennis P M
DP
van Gils
Max Planck Institute for Dynamics and Self Organization, D-37073 Göttingen, Germany and Institute for Nonlinear Dynamics, University of Göttingen, D-37073 Göttingen, Germany and Laboratory of Atomic and Solid-State Physics and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA.
Eberhard
E
Bodenschatz
Max Planck Institute for Dynamics and Self Organization, D-37073 Göttingen, Germany and Department of Physics, University of California, Santa Barbara, California 93106, USA.
Guenter
G
Ahlers