Bounds for Turbulent Transport
نویسنده
چکیده
We would like to pursue a mathematical approach to turbulence that is able to predict bulk average quantities of experimental and practical significance. Among such bulk average quantities, the Nusselt number N , the enhanced bulk average heat transfer due to convection, is perhaps the simplest physical objective of rigorous mathematical study of turbulence. The question we wish to address here is: what are the optimal bounds on N as a function of Rayleigh number R? What is the effect of the Prandtl number? Theoretical results ([1], [2], [3]) predict a maximal ultimate behavior of N ∼ √ R. The experimental ([4]) findings indicate however that
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