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

Shishkina, Olga and Stevens, Richard J.A.M. and Grossmann, Siegfried and Lohse, Detlef (2010) Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution. New Journal of Physics, 12 . 075022. ISSN 1367-2630

Preview

PDF
825Kb

Abstract:	Results on the Prandtl–Blasius-type kinetic and thermal boundary layer (BL) thicknesses in turbulent Rayleigh–Bénard (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 only. It is approximated as for and as for , with . 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 and and grows with the Rayleigh number not slower than . This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations
Item Type:	Article
Copyright:	© IOP Publishing
Faculty:	Science and Technology (TNW)
Research Group:	Physics of Fluids (POF)
Link to this item:	http://purl.utwente.nl/publications/79275
Official URL:	http://dx.doi.org/10.1088/1367-2630/12/7/075022
Export this item as:	BibTeX EndNote HTML Citation Reference Manager

Show download statistics for this publication

Repository Staff Only: item control page

Metis ID: 270424