Fluctuation effects on thermal boundary layer in two-dimensional turbulent Rayleigh-Bénard convection

Abstract

The temperature fields in two-dimensional (2D) Rayleigh-Benard (RB) convection were simulated by the parallel direct method of DNS (PDM-DNS) with different Rayleigh ( Ra ) numbers and different Prandtl ( Pr ) numbers. Mean temperature profiles in terms of one parameter c can be obtained by Shishkina et al. [Phys Rev Lett, 2015, 114: 114302], who developed the temperature boundary layer theory considering fluctuation effect. The relationship of parameter c with Ra and Pr was studied systematically. The characteristics of parameters c report the fluctuation effects on the temperature profiles. For the different Ra with specific Pr , the parameter c are small and little change with Ra at Pr = 4.3, and are large and decrease with the increase of Ra at Pr = 50.0. For a fixed Ra = 1010, the parameter c increases with increasing Pr . This dependence could be described by a power low with an exponent α =0.15 when Pr ≥4.3. The dependences of the parameter c with Pr at different fixed Ra by the different power low take shape as a fan, and their exponents decrease with increasing Ra . The results demonstrate that the fluctuation effects on thermal boundary layer are stronger for smaller Pr where Ra numbers has less influence, weaker for larger Pr and will be enhanced with increasing Ra .