Zusammenfassung
Thermally driven fluid motion usually involves significant variations in
transport properties like viscosity and thermal conductivity.
In the context of Rayleigh-Bénard convection (flow
in a container heated from below and cooled from above), such variations
can break the top-down symmetries of the velocity, temperature, and
density profiles. This symmetry breaking is indicated
by the difference $T_c - T_m$, where $T_c$ is the temperature
in the center of the convection container and $T_m = (T_b + T_t)/2$ is the mean temperature between the bottom ($T_b$) and top ($T_t$) plates.
On the basis of boundary-layer equations with variable transport properties 1-2, we compute $T_c - T_m$ as function of
$\Delta = T_b - T_t$. Two different fluids are considered:
gaseous ethane close to its critical point 1 and water 2.
The latter exhibits $T_c > T_m$ for increasing $\Delta$, meaning that
the top boundary-layer becomes thicker than its counterpart at the bottom plate. In contrast, when working fluid is gaseous ethane, the opposite symmetry breaking is observed.
In both cases, our theoretical results are in reasonable
agreement with experimental measurements (see figure 1).
References
1) G. Ahlers, F. Fontenele Araujo, D. Funfschilling, S. Grossmann,
and D. Lohse. Physical Review Letters 98, 054501 (2007).\\
2) G. Ahlers, E. Brown, F. Fontenele Araujo, D. Funfschilling,
S. Grossmann, and D. Lohse. Journal of Fluid Mechanics 569, 409 (2006)
Nutzer