Space-time correlations in turbulent Rayleigh-Bénard convection

Abstract

The recent development of the elliptic model (He, et al. Phy. Rev. E, 2006), which predicts that the space-time correlation function C u (r, τ) in a turbulent flow has a scaling form C u (r E , 0) with r E being a combined space-time separation involving spatial separation r and time delay τ, has stimulated considerable experimental efforts aimed at testing the model in various turbulent flows. In this paper, we review some recent experimental investigations of the space-time correlation function in turbulent Rayleigh-Benard convection. The experiments conducted at different representative locations in the convection cell confirmed the predictions of the elliptic model for the velocity field and passive scalar field, such as local temperature and shadowgraph images. The understanding of the functional form of C u (r, τ) has a wide variety of applications in the analysis of experimental and numerical data and in the study of the statistical properties of small-scale turbulence. A few examples are discussed in the review.