PREPRINT
6B6DA910-7636-4DE1-801F-46FD633B21C4

Fluctuations of temperature gradients in turbulent thermal convection

K. R. Sreenivasan, A. Bershadskii, J. J. Niemela
arXiv:nlin/0503045

Submitted on 22 March 2005

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.

Preprint

Subjects: Nonlinear Sciences - Chaotic Dynamics; Astrophysics; Condensed Matter - Statistical Mechanics

URL: https://arxiv.org/abs/nlin/0503045