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

Olga Shishkina, Richard J.A.M. Stevens, Siegfried Grossmann, Detlef Lohse

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173 Citations (Scopus)
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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
Original languageEnglish
Article number075022
Number of pages17
JournalNew journal of physics
Volume12
Issue number7
DOIs
Publication statusPublished - 2010

Keywords

  • IR-79275
  • METIS-270424

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