Transitions in convective turbulence: The role of thermal plumes

Itamar Procaccia, Emily S.C. Ching, Peter Constantin, Leo P. Kadanoff, Albert Libchaber, Xiao Zhong Wu

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Abstract

Experiments on convective turbulence have revealed a number of unexpected changes in measured signals. Most notable are (i) the transition from soft to hard turbulence at Rayleigh number (Ra) of about 108, which is seen as a qualitative change in the statistics of temperature fluctuations; (ii) a transition at Ra of about 1011, seen in the power spectra of temperature fluctuations measured at the center of the experimental cell; and (iii) a change, at Ra of about 1013, in the power spectra of a probe placed 0.2 cm from the bottom boundary. In this paper we present experimental evidence for the last two changes and offer a unified mechanism for all these transitions. The main ingredient of our theoretical analysis is a calculation suggesting that isothermal surfaces wrinkle, or appear fractal, above an inner scale. This inner scale and the Hausdorff dimension of the isothermal surfaces are estimated theoretically. This scale diminishes upon increasing Rayleigh number. We argue that as it diminishes it goes through the relevant scales of this experiment, i.e., the height of the central probe, the size of the mixing zone, and the height of the bottom probe. Thus it is suggested that all these transitions may be but different manifestations of the very same physics.

Original languageEnglish (US)
Pages (from-to)8091-8102
Number of pages12
JournalPhysical Review A
Volume44
Issue number12
DOIs
StatePublished - Jan 1 1991

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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    Procaccia, I., Ching, E. S. C., Constantin, P., Kadanoff, L. P., Libchaber, A., & Wu, X. Z. (1991). Transitions in convective turbulence: The role of thermal plumes. Physical Review A, 44(12), 8091-8102. https://doi.org/10.1103/PhysRevA.44.8091