Conditional statistics of temperature fluctuations in turbulent convection

Abstract

We find that the conditional statistics of temperature difference at fixed values of the locally averaged temperature dissipation rate in turbulent convection become Gaussian in the regime where the mixing dynamics is expected to be driven by buoyancy. Hence, intermittency of the temperature fluctuations in this buoyancy-driven regime can be solely attributed to the variation of the locally averaged temperature dissipation rate. We further obtain the functional behavior of these conditional temperature structure functions. This functional form demonstrates explicitly the failure of dimensional arguments and enhances the understanding of the temperature structure functions.

Velocity difference statistics in turbulence

“…2/3 , in accord with experimental observations [31,32,33]. Kolmogorov [8], Obukhov [9] and Castaing [14] assumed a log-normal distribution of ε r ,…”

Scaling behavior in turbulent Rayleigh-Bénard convection revealed by conditional structure functions

“…We have used such conditional structure functions [27] and similar conditional structure functions evaluated at given values of the local temperature variance transfer rate [28] or the local energy transfer rate [29] to examine the validity of the refined similarity hypothesis. Conditional statistics evaluated at a given large-scale velocity have also been used to study the effect of large-scale velocity on inertial-range turbulent statistics [30,31].…”

Locally averaged thermal dissipation rate in turbulent thermal convection: A decomposition into contributions from different temperature gradient components

“…An extension of K62 to turbulent convection leads to the proposal that a scale-dependent locally averaged thermal dissipation ⑀ T ͑l͒ would give rise to an anomalous scaling for the velocity and temperature increments. 11,12 Similarly, an extension of Kraichnan's proposal would lead to the statement that the origin of anomalous scaling is due to a scale-dependent transfer rate of the local temperature-variance. Indeed, the latter proposal was shown to be valid in a recent numerical study of the shell model for homogeneous turbulent convection.…”

“…A large amount of theoretical, 11,12,[16][17][18][19][20][21] numerical, [22][23][24][25][26] and experimental [27][28][29][30][31][32][33][34][35][36] work has been devoted to the study of small-scale fluctuations in turbulent convection. Details about these studies have been reviewed recently by Lohse and Xia.…”