Local Heat Transport in Turbulent Rayleigh-Benard Convection

An important issue in the study of turbulent thermal convection is to understand how heat is transported vertically through a convection cell. Many global heat transport measurements have been carried out in various convecting fluids. These measurements have stimulated considerable theoretical efforts, aimed at explaining the functional form of the measured total heat flux as a function of the Rayleigh number Ra and the Prandtl number Pr. A main issue of an unresolved theoretical debate is whether the heat transport is determined primarily by thermal plumes or by the large-scale circulation. To answer this question, we have recently conducted simultaneous velocity and temperature measurements, from which we obtain the local convective heat flu XJ_z(r) in the vertical direction over varying Ra and spatial position r across the entire cell [PRL, vol. 9,074501 (2003)]. It is found that the vertical heat flux concentrates in the sidewall region and the flux profile remains invariant with Ra. The vertical heat flux at the cell center is small but is definitely non-zero. It accounts approximately for 5% of the peak value near the sidewall. The measurements suggest that the dynamics in turbulent convection is determined primarily by the thermal plumes. The spatial separation of warm and cold plumes and the resulting large-scale circulation provide a fast channel along the cell periphery for the transport of heat. Because velocity fluctuations in the central region are strong, most thermal plumes are mixed up in the region. Nevertheless, there are still some un-mixed warm and cold plumes remained, which give rise to a non-zero J_z in the region. The experiment, therefore, settles a long-debating issue on how heat is transported in small aspect-ratio cells. This work was supported in part by the NSF grant DMR-0071323