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Carnegie Mellon NSF logoCenter for Nonlinear Analysis
Hans Johnston
Afilliation: Dept. of Math & Stat, UMass Amherst

Title: Numerical Study of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux

Abstract: We report the results of high resolution direct numerical simulations of two-dimensional Rayleigh-B\'enard convection for Rayleigh numbers up to Ra$=10^{10}$ in order to study the influence of temperature boundary conditions on turbulent heat transport. Specifically, we consider the extreme cases of fixed heat flux (where the top and bottom boundaries are poor thermal conductors) and fixed temperature (perfectly conducting boundaries). Both cases display identical heat transport at high Rayleigh numbers fitting a power law $\nu \approx 0.138 \times$ Ra $^{.285}$ with a scaling exponent indistinguishable from $2/7 = 0.2857\dots$ above Ra $= 10^{7}$. The overall flow dynamics for both scenarios, in particular the time averaged temperature profiles, are also indistinguishable at the highest Rayleigh numbers. The findings are compared and contrasted with results of recent three-dimensional simulations and experiments. This is joint work with C.R. Doering (U. Michigan), Cheng Wang (U Mass-Dartmouth) and Jian-Guo Liu (Duke).