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Fluctuations of temperature gradients in turbulent thermal convection

K. R. Sreenivasan1, A. Bershadskii1,2, and J. J. Niemela1

  • 1International Center for Theoretical Physics, Strada Costiera 11, I-34100 Trieste, Italy
  • 2ICAR, P.O. Box 31155, Jerusalem 91000, Israel

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Phys. Rev. E 71, 035302(R) – Published 15 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.035302

Abstract

Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature fluctuation T, except that the velocity field in the new equation is substantially smoothed. This smoothed field leads to a −1 scaling of the spectrum of G in the same range of scales for which the spectral exponent of T lies between −7∕5 and −5∕3. This result is confirmed by measurements in a confined container with cryogenic helium gas as the working fluid for Rayleigh number Ra=1.5×1011. Also confirmed is the logarithmic form of the autocorrelation function of G. The anomalous scaling of dissipation-like quantities of T and G are identical in the inertial range, showing that the analogy between the two fields is quite deep.

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Information

Phys. Rev. E 71, 035302(R)– Published 15 March, 2005
  • Received 29 June 2004

© 2005 American Physical Society

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