Heat transport and dynamics of the large-scale circulation of turbulent Rayleigh-Benard convection.

摘要

Experimental studies of turbulent Rayleigh-Benard convection in cylindrical water-filled containers of equal height and diameter, with an applied vertical temperature difference DeltaT are presented.; High-precision measurements of the heat flux Q were shown to agree with the Grossman-Lohse (GL) scaling model of thermal convection for small DeltaT, but for large DeltaT a regime was reached where Q ∝ DeltaT 1/3 in disagreement with the GL model. A prediction that the heat transport in the fluid would be reduced for endplates with finite conductivity was confirmed by switching out plates with different thermal conductivities. The effect of the spatial variation of fluid properties with temperature was measured by comparing experiments in samples of different sizes with the same dimensionless control parameters but different DeltaT.; Thermistors on the sidewall were used to measure various aspects of the large-scale circulation (LSC). The turnover and an azimuthally twisting oscillatory mode were found to have the same frequency for small DeltaT which agrees with the GL model, but the frequencies were found to differ from each other and from the GL model for large DeltaT. The azimuthal orientation theta0(t) of the LSC was found to meander in time as a diffusive process over long time scales. In addition it contained spontaneous events in which the orientation changed by a large angle Deltatheta, either by a rotation of the circulation plane, or by a cessation of the circulation followed by a restart in a randomly chosen direction as seen by the uniform probability distribution p(Deltatheta). Rotations occurred with a monotonically decreasing p(Deltatheta). The distribution of rotations and cessations in time followed Poissonian statistics.; Also presented is a model of the dynamics of the LSC consisting of a pair of stochastic differential equations motivated by the Navier-Stokes equations. The equations have terms representing buoyancy, drag, and angular momentum of the LSC. Stochastic terms phenomenologically represent turbulent fluctuations. This model produces rotations and cessations as observed in experiments. The effect of Earth's Coriolis force on the LSC is included in the model to describe a net azimuthal rotation of the LSC and a preferred azimuthal orientation which were observed in the experiments.