Statistics of the locally averaged thermal dissipation rate in turbulent Rayleigh–Bénard convection

Abstract

From the measured thermal dissipation rate in turbulent Rayleigh–Bénard convection in a cylindrical cell, we construct a locally averaged thermal dissipation rate χ _fτ by averaging over a time interval τ. We study how the statistical moments ⟨(χ _fτ) ^p ⟩ depend on τ at various locations along the vertical axis of the convection cell. We find that ⟨(χ _fτ) ^p ⟩ exhibits good scaling in τ, of about a decade long, with scaling exponents μ(p) for p = 1–6. For Rayleigh number (Ra) around 8×10⁹, the scaling range is 1.4–21 s at the cell center and 4–21 s at the bottom plate. The dissipative and turnover times are about 0.8 s and 35 s respectively, while the timescale corresponding to the local Bolgiano scale is estimated to be about 31 s at the cell center and 3.5 s at the bottom plate. On the basis of several assumptions, we derive theoretical predictions for μ(p) at the different locations. The measured values of μ(p) are presented and shown to be in good agreement with our theoretical predictions.

Keywords:

• turbulent convection

Acknowledgments

The authors acknowledge support by the Hong Kong Research Grants Council under grant nos. CA05/06.SC01 (ESCC and PT), CUHK-400708 (ESCC), and HKUST-602907 (PT).

Notes

1. We note that the statistics of a passive scalar in a wind tunnel have also been studied using the hierarchical structure model, and the corresponding parameter for the codimension of the most intermittent structures was reported to be 0.8±0.1 (see [26]).