Research ArticleGEOPHYSICS

Mechanism of large-scale flow reversals in turbulent thermal convection

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Science Advances  21 Nov 2018:
Vol. 4, no. 11, eaat7480
DOI: 10.1126/sciadv.aat7480
  • Fig. 1 Characterization of the massive eruption events of thermal plumes.

    (A and B) Typical shadowgraph images I(x, y, t) of the convecting fluid at (A) the long steady state and (B) short eruption state. (C) Time series of the measured ζ(t) over a 9-hour-long period of time t. (D) Expanded view of ζ(t) during a massive eruption event of thermal plumes. (E) Corresponding time series of the measured angular momentum L(t) of the LSC. All the measurements are made in water (Pr = 4.4) with Ra = 6.2 × 109.

  • Fig. 2 Statistical properties of the massive eruption events of thermal plumes.

    (A) Normalized histogram H(ζ)/H0 of the measured ζ in water (Pr = 4.4) with Ra = 6.2 × 109. The black squares are obtained from the whole time series containing both the long steady state and short eruption state. The red circles are obtained when only the dataset in the long steady state is included. (B) Measured H(ζ)/H0 in the 10% glycerin solution (Pr = 5.7) with Ra = 4.1 × 109. The black squares are obtained from the whole time series data, and the red circles are obtained when only the long steady state data are included. (C) Normalized most probable heat accumulation (δJ)p/J0 as a function of Ra for water (black squares), 10% glycerin solution (red circles), and 20% glycerin solution (blue triangles). The error bars show the experimental uncertainty of the measurements.

  • Fig. 3 Ra dependence of the PDF of the massive eruption events.

    (A to C) Measured PDF P) (open symbols) as a function of the normalized variable ζ≡ζ/σζ with different values of Ra for (A) water (Pr = 4.4), (B) 10% glycerin solution (Pr = 5.7), and (C) 20% glycerin solution (Pr = 7.6). The solid lines show the fits of the GEV distribution in Eq. 3 to the data points with (A) χ = −0.001, (B) χ = −0.04, and (C) χ = −0.07, respectively.

  • Fig. 4 Statistical properties of the time interval τ between adjacent eruption events.

    (A) Normalized histogram H(τ)/H0 as a function of τ for the 10% glycerin solution at four different values of Ra. The error bars indicate the SD of the measurements. The color-coded lines show the exponential fits, H(τ)/H0 ≃ exp(−τ/τ0), to the data points with τ0 = 2430 s (black solid line), 3150 s (red dashed line), 4140 s (green short dashed line), and 5600 s (blue dotted line). (B) Obtained mean time interval τ0 between adjacent eruption events as a function of Ra for three different fluids: water (blue triangles), 10% glycerin solution (red circles), and 20% glycerin solution (black squares). The error bars show the experimental uncertainty of the measurements. The solid lines (color coded) are the power-law fits, τ0 = aRaβ, to the data points, with a = 0.0092 and β = 0.57 ± 0.1 for the red circles and a = 0.005 and β = 0.57 ± 0.1 for the black squares.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/11/eaat7480/DC1

    Fig. S1. End view of the actual convection cell used in the experiment.

    Fig. S2. Measured Nusselt number Nu as a function of Ra for water in the thin disc cell.

    Fig. S3. Experimental setup of the shadowgraphic measurement.

    Fig. S4. Background and typical turbulent shadowgraphic images.

    Fig. S5. Arrangement of the 12 thermistors on the circular end wall for the measurement of LSC.

    Fig. S6. An example of temperature variations measured by the 12 thermistors as a function of their azimuthal angle θ.

    Fig. S7. Time evolution of the obtained θ0(t) for two characteristic eruption events.

    Movie S1. Measured shadowgraphic movie showing a reversal event of the large-scale circulation in the thin disc cell.

  • Supplementary Materials

    The PDF file includes:

    • Fig. S1. End view of the actual convection cell used in the experiment.
    • Fig. S2. Measured Nusselt number Nu as a function of Ra for water in the thin disc cell.
    • Fig. S3. Experimental setup of the shadowgraphic measurement.
    • Fig. S4. Background and typical turbulent shadowgraphic images.
    • Fig. S5. Arrangement of the 12 thermistors on the circular end wall for the measurement of LSC.
    • Fig. S6. An example of temperature variations measured by the 12 thermistors as a function of their azimuthal angle θ.
    • Fig. S7. Time evolution of the obtained θ0(t) for two characteristic eruption events.

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Measured shadowgraphic movie showing a reversal event of the large-scale circulation in the thin disc cell.

    Files in this Data Supplement:

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