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Results on the Prandtl-Blasius type kinetic and thermal boundary layerthicknesses in turbulent Rayleigh-B\'enard convection in a broad range ofPrandtl numbers are presented. By solving the laminar Prandtl-Blasius boundarylayer equations, we calculate the ratio of the thermal and kinetic boundarylayer thicknesses, which depends on the Prandtl number Pr only. It isapproximated as $0.588Pr^{-1/2}$ for $Pr\ll Pr^*$ and as $0.982 Pr^{-1/3}$ for$Pr^*\ll\Pr$, with $Pr^*= 0.046$. Comparison of the Prandtl--Blasius velocityboundary layer thickness with that evaluated in the direct numericalsimulations by Stevens, Verzicco, and Lohse (J. Fluid Mech. 643, 495 (2010))gives very good agreement. Based on the Prandtl--Blasius type considerations,we derive a lower-bound estimate for the minimum number of the computationalmesh nodes, required to conduct accurate numerical simulations of moderatelyhigh (boundary layer dominated) turbulent Rayleigh-B\'enard convection, in thethermal and kinetic boundary layers close to bottom and top plates. It is shownthat the number of required nodes within each boundary layer depends on Nu andPr and grows with the Rayleigh number Ra not slower than $\sim\Ra^{0.15}$. Thisestimate agrees excellently with empirical results, which were based on theconvergence of the Nusselt number in numerical simulations.

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