SCALING LAWS OF TEMPERATURE AND VELOCITY FLUCTUATIONS IN TURBULENT THERMAL CONVECTION

Experiments by Castaing et al. (1989) showed that the Nusselt number versus Rayleigh number power law scaling exponent in Rayleigh-Benard convection is 2/7 rather than the classical 1/3 over a large range of Rayleigh number (10⁷−-10¹²). They derived two scaling theories (λ-I and λ-II) that result in the 2/7 power law scaling. Adrian (1996) derived corresponding scaling laws for the vertical profiles of the r.m.s. temperature and velocity fluctuations, and provided experimental evidence in support of the λ-layer scalings. However, due to the scatter in the experimental data for the r.m.s. temperature profiles in unsteady non-penetrative convection, the data was not able to select between the two λ-layer scalings. The present set of experiments in Rayleigh-Benard convection were conducted to provide a set of well-converged data that might support of the λ-layer scalings. However, the r.m.s. data over the outer layer do not conclusively select between the λ-I and λ-II scalings. The data are fit by a power-law with exponent −0.4, not with the −1/2 exponent required by the λ-I theory. And, the log-law required by the λ-II theory was found not to be a good fit to the data. Thus, neither of the theories adequately describes the temperature fluctuation data.