Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution

Results on the Prandtl-Blasius-type kinetic and thermal boundary layer (BL) thicknesses in turbulent Rayleigh-Benard (RB) convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl-Blasius BL equations, we calculate the ratio between the thermal and kinetic BL thicknesses, which depends on the Prandtl number Pr only. It is approximated as 0.588Pr(-1/2) for Pr << Pr* and as 0.982Pr(-1/3) for Pr* << Pr, with Pr* equivalent to 0.046. Comparison of the Prandtl-Blasius velocity BL thickness with that evaluated in the direct numerical simulations by Stevens et al (2010 J. Fluid Mech. 643 495) shows very good agreement between them. Based on the Prandtl-Blasius-type considerations, we derive a lower-bound estimate for the minimum number of computational mesh nodes required to conduct accurate numerical simulations of moderately high (BL-dominated) turbulent RB convection, in the thermal and kinetic BLs close to the bottom and top plates. It is shown that the number of required nodes within each BL depends on Nu and Pr and grows with the Rayleigh number Ra not slower than similar to Ra-0.15. This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations.