Physics of Fluids - Publications

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

arΧiv
New Journal of Physics 12, 075022 (2010)

Authors

	Olga Shishkina
	Richard Stevens
	Siegfried Grossmann
	Detlef Lohse

BibTeΧ

@article{1367-2630-12-7-075022,
  author={Olga Shishkina and Richard J A M Stevens and Siegfried Grossmann and Detlef Lohse},
  title={Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution},
  journal={New Journal of Physics},
  volume={12},
  number={7},
  pages={075022},
  url={http://stacks.iop.org/1367-2630/12/i=7/a=075022},
  year={2010},
  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 ##IMG## [http://ej.iop.org/images/1367-2630/12/7/075022/nj355952ieqn1.gif] {{\cal P}\!r} only. It is approximated as ##IMG## [http://ej.iop.org/images/1367-2630/12/7/075022/nj355952ieqn2.gif] {0.588{\cal P}\!r^{-1/2}} for ##IMG## [http://ej.iop.org/images/1367-2630/12/7/075022/nj355952ieqn3.gif] {{\cal P}\!r\ll{\cal P}\!r^*} and as ##IMG## [http://ej.iop.org/images/1367-2630/12/7/075022/nj355952ieqn4.gif] {0.982{\cal P}\!r^{-1/3}} for ##IMG## [http://ej.iop.org/images/1367-2630/12/7/075022/nj355952ieqn5.gif] {{\cal P}\!r^*\ll{\cal P}\!r} , with ##IMG## [http://ej.iop.org/images/1367-2630/12/7/075022/nj355952ieqn6.gif] {{\cal P}\!r^*\equiv0.046} . 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 ##IMG## [http://ej.iop.org/images/1367-2630/12/7/075022/nj355952ieqn7.gif] {{\cal N}\!u} and ##IMG## [http://ej.iop.org/images/1367-2630/12/7/075022/nj355952ieqn8.gif] {{\cal P}\!r} and grows with the Rayleigh number ##IMG## [http://ej.iop.org/images/1367-2630/12/7/075022/nj355952ieqn9.gif] {{\cal R}a} not slower than ##IMG## [http://ej.iop.org/images/1367-2630/12/7/075022/nj355952ieqn10.gif] {\sim\!\!{\cal R}a^{0.15}} . This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations.}
}