Abstract:
A set of convection experiments were performed in which
a layer of fluid is heated from below and cooled from above.
The working
fluid, corn syrup, has a viscosity that depends
strongly on temperature. Viscosity within the fluid layer
varies by a factor of 6 to $1.8\times10^3$
in the various experiments.
A total of 28 experiments were performed for
Rayleigh numbers ($Ra$) between $10^4$ and $10^8$
and Prandtl numbers ($Pr$) sufficiently large, $10^3 < Pr < 10^6$,
that the Reynolds number ($Re$) is less than 1;
here, values of $Ra$ and $Pr$ are based on
material properties at the
average of the temperatures at the top and bottom of the fluid layer.
As $Ra$ increases, flow changes from steady to
time-dependent at $Ra>O(10^5)$. As $Ra$ increases further,
large scale flow is gradually
replaced by isolated rising and sinking plumes. At $Ra>O(10^7)$,
there is no evidence for any large scale circulation, and flow consists
only of plumes. Plumes have
mushroom-shaped ``heads'' and continuous ``tails'' attached
to their respective thermal boundary layers.
The characteristic frequency for the formation of these
plumes scales with $Ra^{2/3}$.
In the experiments at the largest $Ra$, the Nusselt number ($Nu$)
is lower than expected, based on
an extrapolation of the $Nu-Ra$ relationship determined at lower $Ra$;
at the highest $Ra$, $Re \rightarrow 1$, and the lower-than-expected $Nu$ is attributed to inertial effects
that reduce plume head speeds.