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Fluctuations of temperature gradients in turbulent thermal convection

K. R. Sreenivasan·A. Bershadskii·J. J. Niemela
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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=1.5x10^{11}. 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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K. R. Sreenivasan, A. Bershadskii, J. J. Niemela. 2005-03-22. Fluctuations of temperature gradients in turbulent thermal convection. https://doi.org/10.1103/physreve.71.035302

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