Cellular Convection with a Raft
Professor
Jack Whitehead
Woods Hole Oceanographic Institution, MA
Numerical calculations are conducted for Rayleigh-Benard
convection with a floating raft in the Rayleigh number range up to
20,000. The raft is either maintained at a fixed temperature or it is
thermally insulating. The Prandtl number is infinite, flow is two-
dimensional, the Boussinesq approximation is used and in some cases
internal heat generation is included. With chamber aspect ratio 1 and
with raft size fixed, for a small float temperature Tr the raft is
swept to one side and remains pinned there by a steady flow. For
moderate Tr the raft travels back and forth periodically (oscillates)
during which the convection cell alternates direction. For larger Tr,
there
are two oscillating cells of different sizes with sinking at both
walls. The raft exhibits smaller oscillation with the position offset
from the center of the tank. As Tr gets larger the oscillation
amplitude becomes progressively smaller until finally the raft is
stationary near the side of the tank, and as Tr
increases the raft position moves toward the center of the tank. There
is sinking to a shallow depth at both walls, with stratified fluid
below. Next, runs with insulated rafts are conducted. They have the
benefit of possessing only three dimensionless numbers, Rayleigh number
(Ra), scaled raft width, and chamber width to depth aspect ratio. For
aspect ratio=1, oscillation exist for a range of raft widths in the
range 800<Ra<8000. For the range 8000<= Ra < 20, 000 the
raft is pinned to the wall and remains stationary after a brief
adjustment period for all widths. Runs with an aspect ratio of 2 and 4
have no oscillations in the range covered so far ( Ra <= 8000 ).
There are also exploratory examples of hysteresis and irregular
behavior, but the entire parameter range for these effects is not yet
documented.