Cellular convection in a chamber with a warm surface raft

We calculate velocity and temperature fields for Rayleigh-Benard convection in a chamber with a warm raft that floats along the top surface for Rayleigh number up to Ra = 20 000. Two-dimensional, infinite Prandtl number, Boussinesq approximation equations are numerically advanced in time from a motionless state in a chamber of length L' and depth D'. We consider cases with an insulated raft and a raft of fixed temperature. Either oscillatory or stationary flow exists. In the case with an insulated raft over a fluid, there are only three parameters that govern the system: Rayleigh number (Ra), scaled chamber length (L = L'/D'), and scaled raft width (W). For W = 0 and L = 1, linear theory shows that the marginal state without a raft is at a Rayleigh number of 2(3)pi(4) = 779.3, but we find that for the smallest W (determined by numerical grid size) the raft approaches the center monotonically in time for Ra < 790. For 790 < Ra < 811, the raft has a decaying oscillation consisting of raft movement back and forth accompanied by convection cell reversal. For 811 < Ra < 871, the oscillation amplitude is constant in time and it increases with larger Ra. Finally, there is no raft motion for Ra > 871. For larger raft widths, there is a range of W that produces raft oscillation at each Ra up to 20 000. Rafts in longer cavities (L = 2 and 4) have almost no oscillatory behavior. With a raft of temperature set to different values of T-r rather than insulating, a fixed Rayleigh number Ra = 20000, a square chamber (L = 1), fixed raft width, and with internal heat generation, there are two ranges of oscillating flow. (C) 2011 American Institute of Physics. [doi:10.1063/1.3651341]