BOUNDARY-LAYER STABILITY AND HEAT-FLUX IN RAYLEIGH-BENARD EXPERIMENTS

In a series of recent experiments on Rayleigh-Benard convection, the scaling law N approximately R0.29 for the heat flux N was obtained. It characterizes a regime that may be called "submarginal". An important difficulty remains despite the recent theories of Castaing et al., [J. Fluid Mech., 204, 1989, p. 1] and Shraiman and Siggia [Phys. Rev. A, 42, 1990, p. 3650]. It is not known how to predict the transition from this submarginal regime to the classical marginal regime N approximately R1/3 which is also observed in the experiments. Using a stability analysis, it is possible to show that the submarginal regime leads to unstable boundary layers for R < R(I) approximately 5.3 x 10(7) sigma-4. This number corresponds to the transitions observed in water. The boundary layer waves observed in the experiments may be the modes investigated in the stability analysis.