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Turbulence and Shear Flow Phenomena -1 First International Symposium

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Ronald J. Adrian
Laboratory for Turbulence and Complex Flow Department of Theoretical and Applied Mechanics University of Illinois at Urbana-Champaign, Urbana, IL 61801; Department of Mechanical and Aerospace Engineering Arizona State University Tempe, Arizona 85287, USA

Richard L. Fernandes
Department of Theoretical and Applied Mechanics University of Illinois at Urbana-Champaign Urbana, IL 61801, USA


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.