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.