Details about the convection cell used in this experiment have been described elsewhere (27, 35), and here, we only mention some key points. As shown in fig. S1, the convection cell has a shape of thin vertical disc, with its circular cross section aligned parallel to gravity. The top and bottom one-third of the circular sidewall are made of 8-mm-thick copper. The surface of the copper plates in contact with the convecting fluid was electroplated with a thin layer of nickel. The remaining one-third of the sidewall on both sides are made of transparent 18-mm-thick Plexiglas. The two flat end walls of the cell are also made of the same type of Plexiglas. Two silicon rubber film heaters connected in parallel were sandwiched on the back side of the bottom conducting plate to provide constant and uniform heating. The top copper plate is in contact with a cooling chamber consisting of two water channels. The temperature of the top plate was maintained by a temperature-controlled circulator (NESLAB, RTE740), which circulates cooling water with a temperature stability of 10 mK. The temperature of the top and bottom plates was measured at a rate of 2 Hz by two calibrated thermistors with an accuracy of 5 mK. They were embedded in each plate 1 mm away from the surface of the conducting plate.

In this system, the Rayleigh number is defined as Ra≡ψgΔTD3/(νκ), where g is the gravitational acceleration, ΔT is the temperature difference across the cell height (diameter) D, and Ψ, ν, and κ are the thermal expansion coefficient, kinematic viscosity, and thermal diffusivity of the convecting fluid, respectively. The Prandtl number is defined as Pr = ν/κ, which is fixed for a given fluid. The entire convection cell was placed inside a thermostat box, whose temperature was controlled precisely at (40 ± 0.1)°C, which matches the mean temperature of the bulk convecting fluid. At this temperature, the Prandtl number Pr for the three working fluids used was fixed at 4.4 (water), 5.7 (10 wt % glycerin solution), and 7.6 (20 wt % glycerin solution).

This convection cell has two unique features for the experiment attempted here. First, the cell has a circular cross section without any corner to prevent secondary flows, which may destabilize the LSC (22). The LSC in the circular cross section has a fly-wheel–like structure with a mean rotating speed U0 along a fixed orientation most of the time. Because the flow is confined in a thin circular disc, the LSC in the steady state only has a single mode of its simplest form and no other flow modes can be excited in this quasi–two-dimensional (2D) system. Even with these simplifications, the quasi-2D system still has the key features of turbulent convection, which have been observed in the upright cylinders. In particular, we find that the measured Nusselt number Nu as a function of Ra for water is well described by the power law (see more discussions below)Embedded Image(4)which is consistent with the results obtained in the upright cylinders with a fully developed 3D bulk flow (6). Second, the thin circular cell allows us to use the shadowgraph technique to visualize the large-scale convective flow and to precisely measure the net accumulation or loss of heat flux across the entire cell.