Issue |
Europhys. Lett.
Volume 67, Number 3, August 2004
|
|
---|---|---|
Page(s) | 390 - 396 | |
Section | Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics | |
DOI | https://doi.org/10.1209/epl/i2003-10298-4 | |
Published online | 01 July 2004 |
On the validity of two-dimensional numerical approaches to time-dependent thermal convection
Institut für Geophysik, Universität Münster - Corrensstr. 24, 48149 Münster, Germany
Corresponding author: joergs@uni-muenster.de
Received:
19
August
2003
Accepted:
1
June
2004
High-resolution computer simulations of two-dimensional (2D)
convection are often used to investigate turbulent flows. In this
paper we compare numerical simulations in 2D with
three-dimensional (3D) simulations. We investigate flows at a
fixed Rayleigh number of . The velocity boundary
conditions are rigid for the upper and lower boundary and
stress-free for the side walls. For high values of the Prandtl
number the flow structure and global quantities such as the
Nusselt number (Nu) and the Reynolds number (Re) show similar
behaviour in 3D and 2D simulations. For values of the Prandtl
number smaller than unity, however, the 2D results diverge
strongly form the 3D findings. This is true not only for global
properties (Nu, Re) but also for local properties such as the
structure of the boundary layer and the shapes of the up- and
down-wellings. We relate this behaviour to the different
large-scale structure of the flow and the toroidal component of
the kinetic energy.
PACS: 47.27.Te – Convection and heat transfer / 44.25.+f – Natural convection / 92.60.Ek – Convection, turbulence, and diffusion
© EDP Sciences, 2004
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