Scaling laws in the central region of confined turbulent thermal convection

Abstract

In confined turbulent thermal convection, the velocity is separated into two parts: one that is correlated with some function of the temperature fluctuations, and thus associated with the plume velocity, and the other part, the background velocity, which is uncorrelated with any function of the temperature fluctuations. As a result, one should focus on the plume velocity, and not the whole velocity, and the temperature when studying the scaling behavior. In this paper, a phenomenological theory for the scaling behavior in the central region of confined turbulent thermal convection is presented. The spatial (temporal) plume velocity structure functions are found to have the same scaling behavior as the spatial (temporal) temperature structure functions. For tau> or = taub, where the buoyant scale taub is determined in terms of measurable quantities, the scaling exponents of the temporal temperature structure functions and hence those of the temporal plume velocity structure functions are obtained. These results are checked against experimental measurements, and good agreement is found.