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Abstract:
We report direct numerical simulations (DNS) of the Nusselt number Nu, the vertical profiles of mean temperature Theta(z) and temperature variance Omega(7) across the thermal boundary layer (BL) in closed turbulent Rayleigh-Bdnard convection (RBC) with slippery conducting surfaces (z is the vertical distance from the bottom surface). The DNS study was conducted in three RBC samples: a three-dimensional cuboid with length L = H and width W = H/4 (H is the sample height), and two-dimensional rectangles with aspect ratios Gamma L/H = 1 and 10. The slip length b for top and bottom plates varied from 0 to infinity. The Rayleigh numbers Ra were in the range 10(6) <= Ra <= 10(10) and the Prandtl number Pr was fixed at 4.3. As b increases, the normalised Nu/Nu(0) (Nu(0) is the global heat transport for b = 0) from the three samples for different Ra and Gamma can be well described by the same function Nu/Nu(0) = N-0 tanh(b/lambda(0)) + 1, with N-0 = 0.8 +/- 0.03. Here lambda(0) L/(2Nu(0)) is the thermal boundary layer thickness for b = 0. Considering the BL fluctuations for Pr > 1, one can derive solutions of temperature profiles Theta(z) and Omega(z) near the thermal BL for b >= 0. When b = 0, the solutions are equivalent to those reported by Shishkina et al. (Phys. Rev. Lett., vol. 114, 2015, 114302) and Wang et al. (Phys. Rev. Fluids, vol. 1, 2016, 082301(R)), respectively, for no-slip plates. For b > 0, the derived solutions are in excellent agreement with our DNS data for slippery plates.
