Fluctuations of temperature gradients in turbulent thermal convection.

Phys Rev E Stat Nonlin Soft Matter Phys

International Center for Theoretical Physics, Strada Costiera 11, I-34100 Trieste, Italy.

Published: March 2005

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=1.5x 10(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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http://dx.doi.org/10.1103/PhysRevE.71.035302DOI Listing

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